A361094 E.g.f. satisfies A(x) = exp( 1/(1 - x * A(x)^3) - 1 ).

1, 1, 9, 166, 4717, 182136, 8911549, 528571408, 36864033945, 2956595372416, 268116203622961, 27128338649300736, 3029974270053623941, 370289278173654092800, 49150116757136815109733, 7041536364582774222616576, 1083004122024520209576760369

Offset: 0

Author

Seiichi Manyama, Mar 01 2023

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..322

Crossrefs

Cf. A052873, A361093, A361095, A361096, A361097.

Cf. A212917, A361066.

Programs

Mathematica

Table[n! * Sum[(3*n+1)^(k-1) * Binomial[n-1,n-k]/k!, {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Mar 02 2023 *)

PARI

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

Formula

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

a(n) ~ (5 + sqrt(21))^n * n^(n-1) / (3^(3/4) * 7^(1/4) * 2^n * exp((3 - sqrt(21))/6 + (5 - sqrt(21))*n/2)). - Vaclav Kotesovec, Mar 02 2023