A356632 a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/2^k.

1, 1, 2, 9, 48, 330, 2880, 29610, 362880, 5148360, 83462400, 1535549400, 31614105600, 724183059600, 18307441152000, 507367438578000, 15336404987904000, 502812808754256000, 17805001275629568000, 678167395781763888000, 27681559049033809920000

Offset

0,3

Links

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

Formula

E.g.f.: Sum_{k>=0} x^k / (1 - k*x^2/2).

a(n) ~ Pi * exp((1/LambertW(exp(1)*n/2) - 3)*n/2) * n^(3*n/2 + 1) / (sqrt(1 + LambertW(exp(1)*n/2)) * 2^((n-1)/2) * LambertW(exp(1)*n/2)^((n+1)/2)). - Vaclav Kotesovec, Nov 01 2022

Mathematica

a[n_] := n! * Sum[(n - 2*k)^k/2^k, {k, 0, Floor[n/2]}]; a[0] = 1; Array[a, 21, 0] (* Amiram Eldar, Aug 19 2022 *)

Prog

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

Crossrefs

Cf. A356633, A356634.

Cf. A352944.

Sequence in context: A191005 A257544 A295944 * A375798 A224140 A360103

Adjacent sequences: A356629 A356630 A356631 * A356633 A356634 A356635

Keyword

nonn

Author

Seiichi Manyama, Aug 18 2022

Status

approved