A386467 a(0) = a(1) = 1; a(n) = a(n-1) + a(n-2) + Sum_{k=0..n-1} k * a(k) * a(n-1-k).

1, 1, 3, 11, 56, 353, 2619, 22175, 210077, 2196732, 25104008, 311139385, 4156661566, 59551385285, 910955221547, 14821776943015, 255639834413712, 4659720389150655, 89515541970546889, 1807824383345511646, 38294715773270374886, 849051935815301595992, 19665430140710069083996

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x - x^2 - x^2 * (d/dx A(x)) ).

Prog

(PARI) a_vector(n) = my(v=vector(n+1, i, if(i<=2, 1, 0))); for(i=2, n, v[i+1]=v[i]+v[i-1]+sum(j=0, i-1, j*v[j+1]*v[i-j])); v;

Crossrefs

Cf. A075834, A385287.

Cf. A307733.

Sequence in context: A036760 A000985 A207433 * A094611 A052442 A217034

Adjacent sequences: A386464 A386465 A386466 * A386468 A386469 A386470

Keyword

nonn

Author

Seiichi Manyama, Jul 22 2025

Status

approved