A363481 G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} A(2*x^k) * x^k/k ).

1, 2, 11, 108, 1969, 67542, 4473663, 582167944, 150236569819, 77226088637142, 79235069050108841, 162432444097491547308, 665648716390456030366881, 5454326724964994060395500598, 89374602386639273949112262243227

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..80

Formula

A(x) = B(x)^2 where B(x) is the g.f. of A363480.

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

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d * 2^d * a(d-1) ) * a(n-k).

Prog

(PARI) seq(n) = my(A=1); for(i=1, n, A=exp(2*sum(k=1, i, subst(A, x, 2*x^k)*x^k/k)+x*O(x^n))); Vec(A);

Crossrefs

Cf. A000151, A179469, A179470, A363480.

Sequence in context: A365106 A053988 A141314 * A099933 A098437 A145163

Adjacent sequences: A363478 A363479 A363480 * A363482 A363483 A363484

Keyword

nonn

Author

Seiichi Manyama, Jun 04 2023

Status

approved