A385943 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + k^6) * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 5, 988, 2888933, 59194266336, 5550172939486537, 1812719786900514856960, 1706146365658760367161728617, 4025335006744077207541517795929600, 21392361120121469487882204135345762936461, 235316442953945260569915546964215106936729204224

Offset: 0

Author

Seiichi Manyama, Jul 13 2025

Keywords

• nonn

Crossrefs

Cf. A156326, A385939, A385940, A385941, A385942.

Cf. A385834.

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^6)*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..6} Stirling2(6,k) * x^k * (d^k/dx^k A(x)) ).