A385834 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k^6) * a(k) * a(n-1-k).

1, 1, 3, 200, 146401, 600098283, 9378336443140, 437583801957155730, 51482609496251191260549, 13496011632930307406903060651, 7172374406405634119759727327588155, 7172395923569361382696722735713532276498, 12706358411963754476880803069979932030145242780

Offset: 0

Author

Seiichi Manyama, Jul 09 2025

Keywords

• nonn

Crossrefs

Cf. A088716, A385830, A385831, A385832, A385833.

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^6)*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) - x*Sum_{k=1..6} Stirling2(6,k) * x^k * (d^k/dx^k A(x)) ).