A385843 a(n) = 1 + Sum_{k=0..n-1} k^5 * a(k) * a(n-1-k).

1, 1, 2, 66, 16105, 16507753, 51603272051, 401318681776723, 6745364508844808841, 221038850400001766938953, 13052344129663319516736911260, 1305247465753403752473945799113276, 210212714880649951675343095297590137757, 52307860484508916277278208388919504757392477

Offset: 0

Author

Seiichi Manyama, Jul 09 2025

Keywords

• nonn

Crossrefs

Cf. A143917, A385840, A385841, A385842.

Cf. A385833, A385838.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, j^5*v[j+1]*v[i-j])); v;

Formula

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