A385844 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x^3*A''(x))).

1, 1, 1, 3, 21, 273, 5737, 177919, 7651849, 436186313, 31842549569, 2897710853939, 321648004495773, 42779331295225353, 6716367934603667145, 1229096733282700520799, 259339594018913458094865, 62500870590534491566841265, 17062742827503910747790541249, 5238263128497776755775631825219

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = 1 + Sum_{k=0..n-1} (-k + k^2) * a(k) * a(n-1-k).

Mathematica

terms = 20; A[_] = 0; Do[A[x_] = 1/((1 - x) * (1 - x^3*A''[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]  (* Stefano Spezia, Jul 10 2025 *)

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, sum(k=1, 2, stirling(2, k, 1)*j^k)*v[j+1]*v[i-j])); v;

Crossrefs

Cf. A143917, A385845, A385846.

Cf. A385758, A385762.

Sequence in context: A336809 A066206 A130032 * A174967 A126461 A370741

Adjacent sequences: A385841 A385842 A385843 * A385845 A385846 A385847

Keyword

nonn

Author

Seiichi Manyama, Jul 09 2025

Status

approved