A355074 G.f.: Sum_{n>=0} a(n)*x^n/(n!*4^(n*(n-1)/2)) = exp( Sum_{n>=1} x^n/(n!*4^(n*(n-1)/2)) ).

1, 1, 5, 113, 11265, 4859137, 8966576129, 70171067707393, 2313986342570295297, 319893682564775147012097, 184627527352223449064321581057, 443344010564094761887045848673550337, 4416539344305075410912848824562640662560769

Offset: 0

Author

Seiichi Manyama, Jun 18 2022

Keywords

• nonn

Crossrefs

Cf. A000110, A240936, A355073.

Cf. A355071, A355082.

Programs

PARI

a(n) = n!*4^(n*(n-1)/2)*polcoef(exp(sum(k=1, n, x^k/(k!*4^(k*(k-1)/2)))+x*O(x^n)), n);

PARI

T(n, k) = if(k==1, 1, sum(j=1, n-1, 4^(j*(n-j))*binomial(n-1, j)*T(j, k-1)));
a(n) = if(n==0, 1, sum(k=1, n, T(n, k)));