A355073 G.f.: Sum_{n>=0} a(n)*x^n/(n!*3^(n*(n-1)/2)) = exp( Sum_{n>=1} x^n/(n!*3^(n*(n-1)/2)) ).

1, 1, 4, 55, 2539, 383860, 187659181, 293630900689, 1459799672901004, 22924423319469919651, 1131844225175191511724871, 175015470856131731421651730600, 84480805958219938739735661779357401, 126948830401157131161305967764668449231937

Offset: 0

Author

Seiichi Manyama, Jun 18 2022

Keywords

• nonn

Crossrefs

Cf. A000110, A240936, A355074.

Cf. A355070, A355081.

Programs

PARI

a(n) = n!*3^(n*(n-1)/2)*polcoef(exp(sum(k=1, n, x^k/(k!*3^(k*(k-1)/2)))+x*O(x^n)), n);

PARI

T(n, k) = if(k==1, 1, sum(j=1, n-1, 3^(j*(n-j))*binomial(n-1, j)*T(j, k-1)));
a(n) = if(n==0, 1, sum(k=1, n, T(n, k)));