A074143等
A(1,k) = 1; A(n,k) = k + n * Sum_{j=1..n-1} A(j,k)
が
A(n,k) = (n+2) * a(n-1, k) - (n-1) * a(n-2, k) for n > 3
を満たすことを確認してみた。
M=20;
N=10;
b(n, k) = if(n==1, 1, k+n*sum(j=1, n-1, b(j, k)));
a(n, k) = if(n<4, b(n, k), (n+2)*a(n-1, k)-(n-1)*a(n-2, k));
\\ aとbの値が一致するかどうかを確認
for(k=-5, 5, for(n=1, M, if(a(n, k)!=b(n, k), print([n, k]))));
for(k=-5, 5, print1(k,": "); for(n=1, N, print1(a(n, k),", ")); print);
出力結果
-5: 1, -3, -11, -57, -355, -2555, -20865, -190765, -1931495, -21461055,
-4: 1, -2, -7, -36, -224, -1612, -13164, -120356, -1218604, -13540044,
-3: 1, -1, -3, -15, -93, -669, -5463, -49947, -505713, -5619033,
-2: 1, 0, 1, 6, 38, 274, 2238, 20462, 207178, 2301978,
-1: 1, 1, 5, 27, 169, 1217, 9939, 90871, 920069, 10222989,
0: 1, 2, 9, 48, 300, 2160, 17640, 161280, 1632960, 18144000,
1: 1, 3, 13, 69, 431, 3103, 25341, 231689, 2345851, 26065011,
2: 1, 4, 17, 90, 562, 4046, 33042, 302098, 3058742, 33986022,
3: 1, 5, 21, 111, 693, 4989, 40743, 372507, 3771633, 41907033,
4: 1, 6, 25, 132, 824, 5932, 48444, 442916, 4484524, 49828044,
5: 1, 7, 29, 153, 955, 6875, 56145, 513325, 5197415, 57749055,
