A384680 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)*A(x*A(x)^3) ).

1, 1, 3, 15, 100, 805, 7442, 76750, 866818, 10586499, 138549918, 1929878820, 28459172110, 442421488758, 7225177328165, 123586748434192, 2208493015533530, 41138303109509415, 797178212982793708, 16041390159326400966, 334654194086236031816, 7227174934846895031544

Offset: 0

Author

Seiichi Manyama, Jun 06 2025

Keywords

• nonn

Crossrefs

Column k=1 of A384681.

Cf. A143501, A215505, A384145.

Programs

Mathematica

terms = 22; A[] = 0; Do[A[x] = 1/(1-x*A[x]*A[x*A[x]^3]) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jun 07 2025 *)

PARI

a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n-j+k, j)/(3*n-j+k)*a(n-j, j)));

Formula

See A384681.