OFFSET
0,3
FORMULA
a(n) = Sum_{k=1..n} k^(2*(n-k)) * binomial(n-1,k-1) for n > 0.
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n-1, k-1] * k^(2*(n-k)), {k, 1, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Feb 16 2023 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-k^2*x))^k))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, k^(2*(n-k))*binomial(n-1, k-1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 03 2022
STATUS
approved