A386506 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k^3 * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 3, 79, 8845, 2875301, 2173904341, 3302241027205, 9087841330660905, 41958697476222137161, 306298931820000949752841, 3372659958223293180648888761, 53908617652925799897200239787869, 1211704268213547361986251511514073293, 37286568732242131447316119558759880633085

Offset: 0

Author

Seiichi Manyama, Jul 24 2025

Keywords

• nonn

Crossrefs

Cf. A143925, A386505, A386507, A386508, A386509.

Cf. A385940, A386444.

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

Formula

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