OFFSET
0,3
LINKS
Winston de Greef, Table of n, a(n) for n = 0..385
FORMULA
a(n) = Sum_{k=0..floor(n/3)} (n-2*k)^(n-2*k) * binomial(n-2*k,k).
a(n) ~ n^n * (1 + exp(-2)/n + exp(-4)/(2*n^2)). - Vaclav Kotesovec, Feb 18 2023
MATHEMATICA
nmax = 20; CoefficientList[1 + Series[Sum[(k*x*(1 + x^2))^k, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 18 2023 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x*(1+x^2))^k))
(PARI) a(n) = sum(k=0, n\3, (n-2*k)^(n-2*k)*binomial(n-2*k, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 18 2023
STATUS
approved