A378095 E.g.f. satisfies A(x) = exp( x^3 * A(x) / (1-x)^2 ) / (1-x).

1, 1, 2, 12, 120, 1320, 16200, 234360, 3991680, 77535360, 1678924800, 40142995200, 1053264643200, 30109980700800, 931249403884800, 30979797430982400, 1103292884684390400, 41889177988142284800, 1689202127352118579200, 72105273328152166502400

Offset

0,3

Links

Table of n, a(n) for n=0..19.

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

Formula

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

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

Prog

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

Crossrefs

Cf. A352410, A378094.

Sequence in context: A364422 A286629 A361595 * A370876 A329851 A127112

Adjacent sequences: A378092 A378093 A378094 * A378096 A378098 A378101

Keyword

nonn,new

Author

_Seiichi Manyama_, Nov 16 2024

Status

approved