A386448 G.f. A(x) satisfies A(x) = 1/(1 - x - x^3*A''(x)).

1, 1, 1, 3, 23, 319, 6999, 223725, 9838405, 570440733, 42203958765, 3882243620535, 434771830226307, 58255737747374083, 9203989127308306571, 1693477639607917108953, 359008305377998952818761, 86878355403079952880852217, 23804317478591173659253678809, 7331644401028481860472940727371

Offset: 0

Author

Seiichi Manyama, Jul 22 2025

Keywords

• nonn

Crossrefs

Cf. A075834, A386449, A386450, A386451.

Cf. A385762.

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, sum(k=1, 2, stirling(2, k, 1)*j^k)*v[j+1]*v[i-j])); v;

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (-k + k^2) * a(k) * a(n-1-k).