OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..442
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * binomial(k,2) * a(n-k).
a(n) ~ n! / ((1 + LambertW(1/sqrt(2))) * 2^(n+1) * LambertW(1/sqrt(2))^n). - Vaclav Kotesovec, Aug 08 2021
a(n) = n! * Sum_{k=0..floor(n/2)} k^(n-2*k)/(2^k * (n-2*k)!). - Seiichi Manyama, May 13 2022
MATHEMATICA
nmax = 22; CoefficientList[Series[1/(1 - x^2 Exp[x]/2), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Binomial[k, 2] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}]
PROG
(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1-x^2*exp(x)/2))) \\ Michel Marcus, Aug 06 2021
(PARI) a(n) = n!*sum(k=0, n\2, k^(n-2*k)/(2^k*(n-2*k)!)); \\ Seiichi Manyama, May 13 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 06 2021
STATUS
approved