A378092 E.g.f. satisfies A(x) = exp( x * (1-x) * A(x)^2 ) / (1-x).

1, 2, 11, 118, 1993, 46386, 1376059, 49601014, 2104366513, 102717184546, 5670357524011, 349304240222070, 23754501885783673, 1767641331001915474, 142868173684094891803, 12463599550013379095926, 1167281368458948415748833, 116814664082977998388994370, 12440156205235958837516345419

Offset

0,2

Links

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

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

E.g.f.: exp( -LambertW(-2*x/(1-x))/2 )/(1-x).

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

Prog

(PARI) a(n) = n!*sum(k=0, n, (2*k+1)^(k-1)*binomial(n, k)/k!);

Crossrefs

Cf. A352410, A378093.

Cf. A378041.

Sequence in context: A374140 A130222 A379885 * A197993 A057076 A346650

Adjacent sequences: A378089 A378090 A378091 * A378093 A378094 A378095

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2024

Status

approved