OFFSET
0,3
FORMULA
a(0) = 1; a(n) = Sum_{k=1..floor(sqrt(n))} binomial(n,k^2) * a(n-k^2).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k^2] * a[n - k^2], {k, 1, Floor@Sqrt[n]}]; Array[a, 23, 0] (* Amiram Eldar, Apr 30 2022 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, sqrtint(N), x^k^2/(k^2)!))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, sqrtint(i), binomial(i, j^2)*v[i-j^2+1])); v;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 29 2022
STATUS
approved