A363426 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(3*x^k) * x^k/k ).

1, 1, 3, 30, 840, 68934, 16821865, 12280119400, 26868936914550, 176313989066991255, 3470564614854890465955, 204936840860491674903711726, 36304151491699938200267389259775, 19293550877461959142221066537253871070

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..65

Formula

A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+x^(k+1))^(3^k * a(k)).

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) * d * 3^(d-1) * a(d-1) ) * a(n-k).

Prog

(PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*subst(A, x, 3*x^k)*x^k/k)+x*O(x^n))); Vec(A);

Crossrefs

Cf. A004111, A363425, A363427.

Cf. A363338, A363423.

Sequence in context: A113677 A306092 A174549 * A184575 A229373 A355400

Adjacent sequences: A363423 A363424 A363425 * A363427 A363428 A363429

Keyword

nonn

Author

Seiichi Manyama, Jun 01 2023

Status

approved