A386453 - OEIS

A386453

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} binomial(k+2,3) * a(k) * a(n-1-k).

1, 1, 2, 11, 131, 2888, 107027, 6212005, 534389458, 65203760863, 10889677250198, 2417582805875622, 696275799766601842, 254839529849806176727, 116462397939843834894367, 65452132793842930368844779, 44638474752168615525812508053, 36514339485766910607857620043816

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

FORMULA

G.f. A(x) satisfies A(x) = 1/( 1 - x - x*Sum_{k=1..3} binomial(2,k-1) * x^k/k! * (d^k/dx^k A(x)) ).

PROG

(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, binomial(j+2, 3)*v[j+1]*v[i-j])); v;

CROSSREFS

Cf. A075834, A386452, A386454, A386455.

Cf. A385875.