A377828 E.g.f. satisfies A(x) = (1 + x)^3 * exp(x * A(x)).

1, 4, 21, 193, 2669, 48711, 1113325, 30615019, 984983193, 36319515355, 1510538562641, 69968975169567, 3572684914283941, 199389519518767111, 12075888110164192917, 788850329621989132771, 55289606764547108653361, 4138807268239824817387443, 329564746571982961088975257

Offset: 0

Author

Seiichi Manyama, Nov 09 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A377826, A377827.

Cf. A377741, A377811.

Programs

PARI

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

Formula

E.g.f.: (1+x)^3 * exp( -LambertW(-x*(1+x)^3) ).

E.g.f.: -LambertW(-x*(1+x)^3)/x.

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