A363441 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (2*x)^k/k ).

1, 2, 4, 16, 52, 208, 840, 3520, 15008, 65344, 288408, 1288416, 5813744, 26460800, 121333200, 559991712, 2599385536, 12127405952, 56837861376, 267473333120, 1263354463056, 5987210061184, 28461008374480, 135672151034304, 648406644570048

Offset

0,2

Links

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

Formula

A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+2*x^(k+1))^a(k).

a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-2)^(k/d) * 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, x^k)*(2*x)^k/k)+x*O(x^n))); Vec(A);

Crossrefs

Cf. A004111, A363442, A363443.

Cf. A179469, A363425.

Sequence in context: A153948 A284730 A255730 * A087972 A010362 A262164

Adjacent sequences: A363438 A363439 A363440 * A363442 A363443 A363444

Keyword

nonn

Author

Seiichi Manyama, Jun 02 2023

Status

approved