A385841 a(n) = 1 + Sum_{k=0..n-1} k^3 * a(k) * a(n-1-k).

1, 1, 2, 18, 505, 32857, 4141211, 898723027, 309170208201, 158606268801081, 115783226426053396, 115899337245305115516, 154378153899481307826141, 266920063540268509322880013, 586690612016923635703423527652, 1610466268575965949949881680290412

Offset: 0

Author

Seiichi Manyama, Jul 09 2025

Keywords

• nonn

Crossrefs

Cf. A143917, A385840, A385842, A385843.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, j^3*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x*Sum_{k=1..3} Stirling2(3,k) * x^k * (d^k/dx^k A(x)) ) ).