A374346 E.g.f. A(x) satisfies A(x) = A(x^2)^(1/2) * exp(2*x) with A(0)=1.

1, 2, 6, 20, 88, 432, 2464, 14912, 111360, 912896, 8491264, 80905728, 861835264, 9524264960, 113218762752, 1362387243008, 20665650774016, 337892698226688, 6100999266304000, 106342541313572864, 2014622956858638336, 37864490015441027072

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..200

Formula

E.g.f.: exp( 2 * Sum_{k>=0} x^(2^k)/2^k ).

E.g.f.: 1/( Product_{k>=1} (1 - x^(2*k-1))^(mu(2*k-1)/(2*k-1)) )^2, where mu() is the Moebius function.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*sum(k=0, ceil(log(N+1)/log(2)), x^2^k/2^k))))

Crossrefs

Cf. A005388, A008683, A118393, A308392.

Sequence in context: A004104 A304932 A293032 * A241497 A003069 A079468

Adjacent sequences: A374343 A374344 A374345 * A374347 A374348 A374349

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 05 2024

Status

approved