A309618 a(n) = Sum_{k=0..floor(n/2)} k! * 2^k * (n - 2*k)!.

1, 1, 4, 8, 36, 140, 832, 5376, 42432, 374592, 3720960, 40694784, 486679296, 6310114560, 88168366080, 1320468480000, 21101183631360, 358354687426560, 6444941507297280, 122367252835860480, 2445878526994022400, 51337143210820239360, 1128918790687649955840

Offset: 0

Author

Vaclav Kotesovec, Aug 10 2019

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..448

Crossrefs

Cf. A000142, A003149, A107713, A110143, A309619.

Programs

Mathematica

Table[Sum[k!*2^k*(n-2*k)!, {k, 0, Floor[n/2]}], {n, 0, 25}]
nmax = 25; CoefficientList[Series[Sum[k!*x^k, {k, 0, nmax}] * Sum[k!*2^k*x^(2 k), {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: B(x)*B(2*x^2), where B(x) is g.f. of A000142.

a(n) ~ n! * (1 + 2/n^2 + 2/n^3 + 10/n^4 + 50/n^5 + 250/n^6 + 1442/n^7 + 9514/n^8 + 68882/n^9 + 539098/n^10 + ...), for coefficients see A326983.