A385952 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(k+3,3) * a(k) * a(n-1-k).

1, 1, 5, 59, 1309, 48790, 2840931, 244770680, 29887602613, 4993307581843, 1108754325139526, 319359741512132370, 116893982001130825135, 53422902443413341967604, 30024521959524315980717288, 20477109546794819263709728560, 16750490995674468051531269811269

Offset: 0

Author

Seiichi Manyama, Jul 13 2025

Keywords

• nonn

Crossrefs

Cf. A088716, A351798, A385953, A385954, A385955.

Cf. A385945.

Programs

PARI

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

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - Sum_{k=0..3} binomial(3,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.