A385767 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x)^3 - x^2*A(x)^2*A'(x))).

1, 2, 11, 103, 1240, 17405, 272647, 4652676, 85204285, 1657791964, 34030090459, 733238701637, 16520229963511, 388058679087053, 9481616930642904, 240524381652918706, 6324953229391777117, 172191111285984106951, 4847629590517906310392, 140987258808372483601766

Offset: 0

Author

Seiichi Manyama, Jul 09 2025

Keywords

• nonn

Crossrefs

Cf. A321087, A385766.

Cf. A349289.

Programs

Mathematica

terms = 20; A[] = 0; Do[A[x] = 1/((1-x)*(1-x*A[x]^3-x^2*A[x]^2*A'[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 09 2025 *)

Formula

a(n) = 1 + Sum_{i, j, k, l>=0 and i+j+k+l=n-1} (i+1) a(i) * a(j) * a(k) * a(l).