A377503 - OEIS

%I #12 Oct 31 2024 06:47:53

%S 1,2,18,270,5936,173330,6335772,278724362,14350790064,847007698338,

%T 56397332340020,4182866692785242,342022887565717800,

%U 30570009715185100082,2965368922693150575084,310276298423966343555690,34834957115496822249510752,4177193847524372747798263106

%N E.g.f. satisfies A(x) = 1/(1 - x * exp(x) * A(x))^2.

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A364983.

%F a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(3*k+1,k)/( (k+1)*(n-k)! ).

%o (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(3*k+1, k)/((k+1)*(n-k)!));

%Y Cf. A295238, A377504, A377528.

%Y Cf. A006013, A364983.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 30 2024