A385806 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^4 - x^2*A(x)^3*A'(x)).

1, 1, 6, 56, 656, 8901, 134452, 2210098, 38972064, 730162940, 14436966166, 299765678868, 6512235121216, 147598065921110, 3482200915723080, 85360331346689846, 2170845829694670304, 57202138454461379820, 1559974375525184897080, 43985410131699875744400

Offset: 0

Author

Seiichi Manyama, Jul 09 2025

Keywords

• nonn

Crossrefs

Cf. A182304, A385801.

Cf. A002294.

Programs

Mathematica

terms = 20; A[] = 0; Do[A[x] = 1/(1-x*A[x]^4-x^2*A[x]^3*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, m>=0 and i+j+k+l+m=n-1} (i+1) a(i) * a(j) * a(k) * a(l) * a(m).