OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..floor(n/2)} (n-k)^(2*(n-k)) * binomial(n-k,k).
a(n) ~ n^(2*n). - Vaclav Kotesovec, Feb 16 2023
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n-k, k] * (n-k)^(2*(n-k)), {k, 0, n/2}], {n, 1, 30}]}] (* Vaclav Kotesovec, Feb 16 2023 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x*(1+x))^k))
(PARI) a(n) = sum(k=0, n\2, (n-k)^(2*(n-k))*binomial(n-k, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 15 2023
STATUS
approved