A363443 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (4*x)^k/k ).

1, 4, 16, 128, 864, 6912, 55936, 470016, 4025600, 35144704, 311190784, 2789206016, 25254028288, 230652174336, 2122466561024, 19659305379840, 183146187440128, 1714933158969344, 16131631511164928, 152366562180972544

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..996

Formula

A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+4*x^(k+1))^a(k).

a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-4)^(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)*(4*x)^k/k)+x*O(x^n))); Vec(A);

Crossrefs

Cf. A004111, A363441, A363442.

Cf. A363427, A363440.

Sequence in context: A318152 A358083 A323552 * A349264 A061129 A061131

Adjacent sequences: A363440 A363441 A363442 * A363444 A363445 A363446

Keyword

nonn

Author

Seiichi Manyama, Jun 02 2023

Status

approved