250225

PARI


A059297, A185951 and A136630

最近よく使っている係数を出力してみた。

N=10;

a059297(n, k) = my(x='x+O('x^(n+1)), t='t+O('t^(k+1))); n!*polcoef(polcoef(exp(t*x* exp(x)), n), k);
a185951(n, k) = my(x='x+O('x^(n+1)), t='t+O('t^(k+1))); n!*polcoef(polcoef(exp(t*x*cosh(x)), n), k);
a136630(n, k) = my(x='x+O('x^(n+1)), t='t+O('t^(k+1))); n!*polcoef(polcoef(exp(t  *sinh(x)), n), k);

for(n=0, N, for(k=0, n, print1(a059297(n, k),", ")); print)
for(n=0, N, for(k=0, n, print1(a185951(n, k),", ")); print)
for(n=0, N, for(k=0, n, print1(a136630(n, k),", ")); print)

出力結果

1, 

0, 1, 

0, 2, 1, 

0, 3, 6, 1, 

0, 4, 24, 12, 1, 

0, 5, 80, 90, 20, 1, 

0, 6, 240, 540, 240, 30, 1, 

0, 7, 672, 2835, 2240, 525, 42, 1, 

0, 8, 1792, 13608, 17920, 7000, 1008, 56, 1, 

0, 9, 4608, 61236, 129024, 78750, 18144, 1764, 72, 1, 

0, 10, 11520, 262440, 860160, 787500, 272160, 41160, 2880, 90, 1, 

1, 

0, 1, 

0, 0, 1, 

0, 3, 0, 1, 

0, 0, 12, 0, 1, 

0, 5, 0, 30, 0, 1, 

0, 0, 120, 0, 60, 0, 1, 

0, 7, 0, 735, 0, 105, 0, 1, 

0, 0, 896, 0, 2800, 0, 168, 0, 1, 

0, 9, 0, 15372, 0, 8190, 0, 252, 0, 1, 

0, 0, 5760, 0, 114240, 0, 20160, 0, 360, 0, 1, 

1, 

0, 1, 

0, 0, 1, 

0, 1, 0, 1, 

0, 0, 4, 0, 1, 

0, 1, 0, 10, 0, 1, 

0, 0, 16, 0, 20, 0, 1, 

0, 1, 0, 91, 0, 35, 0, 1, 

0, 0, 64, 0, 336, 0, 56, 0, 1, 

0, 1, 0, 820, 0, 966, 0, 84, 0, 1, 

0, 0, 256, 0, 5440, 0, 2352, 0, 120, 0, 1,