A385833 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k^5) * a(k) * a(n-1-k).

1, 1, 3, 104, 25585, 26276091, 82191698776, 639369308538270, 10747798328839679301, 352216100969784522738455, 20799065226839989441184616755, 2079968920938449464603267217930862, 334987314655287149221766445992266495796, 83356568448492338030736248231384628286761124

Offset: 0

Author

Seiichi Manyama, Jul 09 2025

Keywords

• nonn

Crossrefs

Cf. A088716, A385830, A385831, A385832, A385834.

Cf. A385765, A385843.

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^5)*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) - x*Sum_{k=1..5} Stirling2(5,k) * x^k * (d^k/dx^k A(x)) ).