220625

PARI

A355133等

似た数列を出力してみた。

M=10;

a355133(n) = if(n==0, 1, sum(k=1, n,            k*2^k    *stirling(n, k, 1)*a355133(k-1)));
for(n=0, M, print1(a355133(n), ", "))
b355208(n) = if(n==0, 1, sum(k=1, n,              2^k    *stirling(n, k, 1)*b355208(k-1)));
a355208(n) = b355208(n-1);
for(n=1, M, print1(a355208(n), ", "))

a355134(n) = if(n==0, 1, sum(k=1, n, (-1)^(n-k)*k*2^k    *stirling(n, k, 1)*a355134(k-1)));
for(n=0, M, print1(a355134(n), ", "))
b355209(n) = if(n==0, 1, sum(k=1, n, (-1)^(n-k)  *2^k    *stirling(n, k, 1)*b355209(k-1)));
a355209(n) = b355209(n-1);
for(n=1, M, print1(a355209(n), ", "))

a355131(n) = if(n==0, 1, sum(k=1, n,            k*2^k    *stirling(n, k, 2)*a355131(k-1)));
for(n=0, M, print1(a355131(n), ", "))
b355210(n) = if(n==0, 1, sum(k=1, n,              2^k    *stirling(n, k, 2)*b355210(k-1)));
a355210(n) = b355210(n-1);
for(n=1, M, print1(a355210(n), ", "))

a355132(n) = if(n==0, 1, sum(k=1, n, (-1)^(n-k)*k*2^k    *stirling(n, k, 2)*a355132(k-1)));
for(n=0, M, print1(a355132(n), ", "))
b355211(n) = if(n==0, 1, sum(k=1, n, (-1)^(n-k)  *2^k    *stirling(n, k, 2)*b355211(k-1)));
a355211(n) = b355211(n-1);
for(n=1, M, print1(a355211(n), ", "))

a355120(n) = if(n==0, 1, sum(k=1, n,            k*2^(k-1)*stirling(n, k, 1)*a355120(k-1)));
for(n=0, M, print1(a355120(n), ", "))
b355214(n) = if(n==0, 1, sum(k=1, n,              2^(k-1)*stirling(n, k, 1)*b355214(k-1)));
a355214(n) = b355214(n-1);
for(n=1, M, print1(a355214(n), ", "))

a355121(n) = if(n==0, 1, sum(k=1, n, (-1)^(n-k)*k*2^(k-1)*stirling(n, k, 1)*a355121(k-1)));
for(n=0, M, print1(a355121(n), ", "))
b355215(n) = if(n==0, 1, sum(k=1, n, (-1)^(n-k)  *2^(k-1)*stirling(n, k, 1)*b355215(k-1)));
a355215(n) = b355215(n-1);
for(n=1, M, print1(a355215(n), ", "))

a355122(n) = if(n==0, 1, sum(k=1, n,            k*2^(k-1)*stirling(n, k, 2)*a355122(k-1)));
for(n=0, M, print1(a355122(n), ", "))
b355216(n) = if(n==0, 1, sum(k=1, n,              2^(k-1)*stirling(n, k, 2)*b355216(k-1)));
a355216(n) = b355216(n-1);
for(n=1, M, print1(a355216(n), ", "))

a355123(n) = if(n==0, 1, sum(k=1, n, (-1)^(n-k)*k*2^(k-1)*stirling(n, k, 2)*a355123(k-1)));
for(n=0, M, print1(a355123(n), ", "))
b355217(n) = if(n==0, 1, sum(k=1, n, (-1)^(n-k)  *2^(k-1)*stirling(n, k, 2)*b355217(k-1)));
a355217(n) = b355217(n-1);
for(n=1, M, print1(a355217(n), ", "))

出力結果

1, 2, 14, 292, 16836, 2517888, 927979616, 811623678304, 1639230314891936, 7494183556478948928, 76401967141928846136512, 

1, 2, 6, 28, 236, 4400, 197552, 20430656, 4600591488, 2179887358272, 

1, 2, 18, 484, 33756, 5726688, 2282797376, 2092535127520, 4343501656698208, 20170260943214036928, 207447888426953360929472, 

1, 2, 10, 108, 2308, 94384, 7315728, 1077605632, 304189296192, 166216599473344, 

1, 2, 18, 482, 33554, 5688162, 2266828306, 2077710037986, 4312607047919378, 20026622857699101794, 205970083615742633015314, 

1, 2, 10, 106, 2234, 90570, 6986490, 1026623306, 289475035770, 158101579596106, 

1, 2, 14, 290, 16654, 2487202, 916292622, 801308046114, 1618342215277838, 7398618880762147490, 75427503900622910066190, 

1, 2, 6, 26, 182, 2746, 111350, 11245882, 2521162358, 1193350247226, 

1, 1, 3, 26, 654, 45084, 7934924, 3381663872, 3365978050576, 7632454575648720, 38732162420625498608, 

1, 1, 1, 0, -8, -64, -600, -14104, -1170120, -248815984, 

1, 1, 5, 74, 2778, 248244, 51212444, 23984832416, 25218677193200, 59000757443457072, 304720138059811544048, 

1, 1, 3, 20, 260, 6304, 281096, 23095768, 3534364152, 1022066008944, 

1, 1, 5, 73, 2725, 242921, 50068197, 23441365641, 24644653272869, 57655911504114985, 297771560486880287589, 

1, 1, 3, 19, 239, 5675, 249983, 20404811, 3112376543, 898693573515, 

1, 1, 3, 25, 611, 41721, 7326115, 3120454233, 3105527125475, 7041597540281017, 35733375744777784867, 

1, 1, 1, -1, -19, -153, -1155, -9785, -183075, -25013497,