A378093 E.g.f. satisfies A(x) = exp( x * (1-x)^2 * A(x)^3 ) / (1-x).

1, 2, 13, 187, 4421, 145381, 6106885, 312010217, 18775791529, 1300609323577, 101932831136801, 8917429459192717, 861423205666601869, 91071085791088039781, 10459294205668851438589, 1296711971347861868098561, 172604468588739615868724945, 24551969347625035312300681969

Offset

0,2

Links

Table of n, a(n) for n=0..17.

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

Formula

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

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

Prog

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

Crossrefs

Cf. A352410, A378092.

Cf. A363478.

Sequence in context: A073178 A193192 A356491 * A226865 A062156 A378043

Adjacent sequences: A378090 A378091 A378092 * A378094 A378095 A378096

Keyword

nonn,new

Author

Seiichi Manyama, Nov 16 2024

Status

approved