A363545 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 - 2*x^k)) ).

1, 1, 4, 14, 54, 206, 823, 3312, 13619, 56643, 238569, 1014443, 4352038, 18809992, 81843021, 358186642, 1575810191, 6965004499, 30914431131, 137736012285, 615785575785, 2761693248028, 12421390811559, 56016050571825, 253228531426237

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, A363546, A363580, A363581.

Cf. A362389.

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*(1-2*x^k)))+x*O(x^n))); Vec(A);

Formula

A(x) = (1 - 2*x) * B(x) where B(x) is the g.f. of A362389.

a(n) = A362389(n) - 2*A362389(n-1) for n > 0.