A361093 E.g.f. satisfies A(x) = exp( 1/(1 - x * A(x)^2) - 1 ).

1, 1, 7, 97, 2049, 58541, 2114143, 92419965, 4746108769, 280105517881, 18683156508471, 1389960074426969, 114119472522112225, 10249863809271551973, 999746622121255094479, 105236583967331849218741, 11891012005206169120252737, 1435560112909007680593616625

Offset: 0

Author

Seiichi Manyama, Mar 01 2023

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..334

Crossrefs

Cf. A052873, A361094, A361095, A361096, A361097.

Cf. A212722, A361065.

Programs

Mathematica

Table[n! * Sum[(2*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, (2*n+1)^(k-1)*binomial(n-1, n-k)/k!);

Formula

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

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