A363440 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * (4*x)^k/k ).

1, 4, 32, 256, 2208, 19712, 183808, 1763328, 17332992, 173621248, 1766188288, 18196260864, 189474570240, 1990887063552, 21082432966656, 224766598100992, 2410570956881920, 25988893875994624, 281505478557407232, 3062014088362049536

Offset: 0

Author

Seiichi Manyama, Jun 02 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..938

Crossrefs

Cf. A000081, A179469, A363439.

Cf. A363424.

Programs

PARI

seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, subst(A, x, x^k)*(4*x)^k/k)+x*O(x^n))); Vec(A);

Formula

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