A385832 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k^4) * a(k) * a(n-1-k).

1, 1, 3, 56, 4705, 1218747, 765389596, 994245193386, 2390167881074445, 9797301213263859467, 64309492440202351088387, 643287882516349276270085850, 9420307945482704895570131173916, 195367768417628005309741727943311572, 5580484965405704420901774303244279908840

Offset: 0

Author

Seiichi Manyama, Jul 09 2025

Keywords

• nonn

Crossrefs

Cf. A088716, A385830, A385831, A385833, A385834.

Cf. A385764.

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^4)*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) - x*Sum_{k=1..4} Stirling2(4,k) * x^k * (d^k/dx^k A(x)) ).