A385940 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + k^3) * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 5, 148, 17189, 5676336, 4326290857, 6602349049360, 18222895109730537, 84299882148193513600, 616234715187848381357261, 6792153358905298302629935104, 108647409624774384033524243233165, 2443481854821246436998727854436139008, 75225062360951292682727255438183855480625

Offset: 0

Author

Seiichi Manyama, Jul 13 2025

Keywords

• nonn

Crossrefs

Cf. A156326, A385939, A385941, A385942, A385943.

Cf. A385831.

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

Formula

E.g.f. A(x) satisfies A(x) = exp( x*A(x) + x*Sum_{k=1..3} Stirling2(3,k) * x^k * (d^k/dx^k A(x)) ).