A363424 G.f. satisfies A(x) = exp( Sum_{k>=1} A(4*x^k) * x^k/k ).

1, 1, 5, 85, 5535, 1422815, 1458410395, 5975113492155, 97902240525033630, 6416219161308006188750, 1681979772433159156954845846, 1763685303864317080584539713676102, 7397434088431352859937186709876628421294

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..58

Formula

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

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

Prog

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

Crossrefs

Cf. A000081, A179470, A363423.

Cf. A359186.

Sequence in context: A317355 A018925 A309327 * A174320 A140159 A073862

Adjacent sequences: A363421 A363422 A363423 * A363425 A363426 A363427

Keyword

nonn

Author

Seiichi Manyama, Jun 01 2023

Status

approved