A355071 G.f.: Sum_{n>=0} a(n)*x^n/(n!*4^(n*(n-1)/2)) = log( Sum_{n>=0} x^n/(n!*4^(n*(n-1)/2)) ).

0, 1, -3, 81, -13311, 11688705, -51334027263, 1082183686000641, -106464672910860746751, 47880898685034024043741185, -96901748928702482338511172665343, 871602415363671863767026450797790494721

Offset

0,3

Links

Table of n, a(n) for n=0..11.

Formula

a(0) = 0; a(n) = 1 - Sum_{k=1..n-1} 4^(k*(n-k)) * binomial(n-1,k) * a(n-k).

Prog

(PARI) a(n) = n!*4^(n*(n-1)/2)*polcoef(log(sum(k=0, n, x^k/(k!*4^(k*(k-1)/2)))+x*O(x^n)), n);
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=0; for(i=1, n, v[i+1]=1-sum(j=1, i-1, 4^(j*(i-j))*binomial(i-1, j)*v[i-j+1])); v;

Crossrefs

Cf. A134531, A355070.

Cf. A137435, A355074.

Sequence in context: A207983 A207195 A207215 * A207544 A207311 A206693

Adjacent sequences: A355068 A355069 A355070 * A355072 A355073 A355074

Keyword

sign

Author

Seiichi Manyama, Jun 18 2022

Status

approved