A386444 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} k^3 * a(k) * a(n-1-k).

1, 1, 2, 19, 550, 36314, 4612644, 1005608259, 346940795318, 178328747938574, 130358697631572620, 130619605078238043630, 174116069712361545382300, 301220935342882714418320660, 662385014999576998657776303368, 1818909557774291764795223960949603, 6142458248209027135766781428841480918

Offset: 0

Author

Seiichi Manyama, Jul 22 2025

Keywords

• nonn

Crossrefs

Cf. A075834, A386443, A386445, A386446, A386447.

Cf. A385831.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, j^3*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x - x*Sum_{k=1..3} Stirling2(3,k) * x^k * (d^k/dx^k A(x)) ).