A397881 E.g.f. A(x) satisfies A(x) = 1 + x * exp(x) * A(x * exp(2*x)).

1, 1, 4, 33, 484, 10585, 323646, 13129585, 678943000, 43470568305, 3368920322170, 310239261383161, 33435268999158324, 4163856785789863513, 592763736929971545862, 95571143628449891791425, 17310994946723775632852656, 3497748520992039001264835425, 783435396067546727773400019570

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(0) = 1; a(n) = n * Sum_{k=0..n-1} (2*k+1)^(n-k-1) * binomial(n-1,k) * a(k).

Prog

(PARI) a_vector(n, s=2, t=1) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*sum(k=0, i-1, (s*k+t)^(i-k-1)*binomial(i-1, k)*v[k+1])); v;

Crossrefs

Cf. A006153, A396900.

Cf. A397859.

Sequence in context: A002190 A101981 A002018 * A368837 A219504 A258180

Adjacent sequences: A397874 A397875 A397877 * A397882 A397884 A397886

Keyword

nonn,new

Author

Seiichi Manyama, Jul 13 2026

Status

approved