A363546 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 - 3*x^k)) ).

1, 1, 5, 22, 105, 497, 2431, 11976, 59928, 302816, 1545660, 7955132, 41255625, 215378364, 1131134574, 5972272636, 31684600709, 168824599282, 903080385252, 4848038120323, 26110774945462, 141048622038068, 764026532321068, 4149020129689451

Offset: 0

Author

Seiichi Manyama, Jun 09 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A052855, A198518, A363545, A363580, A363581.

Cf. A363541.

Programs

PARI

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

Formula

A(x) = (1 - 3*x) * B(x) where B(x) is the g.f. of A363541.

a(n) = A363541(n) - 3*A363541(n-1) for n > 0.