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A360727
Expansion of Sum_{k>=0} (k * x * (1 + x^2))^k.
5
1, 1, 4, 28, 264, 3206, 47684, 839249, 17058688, 393216567, 10134918592, 288815780665, 9016571143680, 306027510946208, 11219450971161024, 441846991480590475, 18602901833071633792, 833832341625621777368, 39642569136740054367808
OFFSET
0,3
LINKS
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
Cf. A360730.
Sequence in context: A260775 A292810 A368892 * A353013 A284756 A316144
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 18 2023
STATUS
approved