A376517 E.g.f. satisfies A(x) = exp(x^2 * (1 + x) * A(x)).

1, 0, 2, 6, 36, 360, 3000, 40320, 532560, 8527680, 152591040, 2987107200, 65408333760, 1544664401280, 39767121313920, 1100734899264000, 32661264290054400, 1034874195222067200, 34834463447361177600, 1242657968679512985600, 46804841790705090892800

Offset

0,3

Links

Table of n, a(n) for n=0..20.

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

Formula

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

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

a(n) ~ sqrt((2 + 3*r)/(1 + r)) * n^(n-1) / (exp(n-1) * r^n), where r = (-1 + 2*cosh(log(-1 + (3*(9 + sqrt(81 - 12*exp(1))))/(2*exp(1)))/3))/3. - Vaclav Kotesovec, Sep 26 2024

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x^2*(1+x)))))
(PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(k-1)*binomial(k, n-2*k)/k!);

Crossrefs

Cf. A362771, A376518.

Cf. A376492, A376512.

Sequence in context: A055541 A275551 A321085 * A133822 A133892 A196870

Adjacent sequences: A376514 A376515 A376516 * A376518 A376519 A376520

Keyword

nonn,easy

Author

Seiichi Manyama, Sep 26 2024

Status

approved