A385801 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^3 - x^2*A(x)^2*A'(x)).

1, 1, 5, 39, 385, 4438, 57375, 812720, 12428977, 203183595, 3525740946, 64607354042, 1245332551755, 25172891719156, 532300335665640, 11750901331656240, 270347716681495537, 6472208752084251545, 161016802667814325743, 4157582808082008519225

Offset: 0

Author

Seiichi Manyama, Jul 09 2025

Keywords

• nonn

Crossrefs

Cf. A182304, A385806.

Cf. A385767.

Programs

Mathematica

terms = 20; A[] = 0; Do[A[x] = 1/(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(0) = 1; a(n) = Sum_{i, j, k, l>=0 and i+j+k+l=n-1} (i+1) a(i) * a(j) * a(k) * a(l).