A308392 -id:A308392 - cp's OEIS frontend

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

Seiichi Manyama, Jul 05 2024

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

Cf. A005388, A008683, A118393, A308392.

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))))

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.

A308461 Expansion of e.g.f. exp(x + 2 * Sum_{k>=2} x^(2^k)/2^k).

Original entry on oeis.org

1, 1, 1, 1, 13, 61, 181, 421, 15961, 137593, 682921, 2498761, 77344741, 927575221, 6402167773, 31881065581, 4104839160241, 68050288734961, 609856397747281, 3857727706737553, 222655237411428541, 4351842324095032621, 47276537013742616581, 361153046139022585141

Offset: 0

Ilya Gutkovskiy, May 28 2019

nonn

Cf. A000321, A005388, A008683, A308392.

nmax = 23; CoefficientList[Series[Exp[x + 2 Sum[x^(2^k)/2^k, {k, 2, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Product[(1 + (-x)^k)^((-1)^k MoebiusMu[k]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

E.g.f.: Product_{k>=1} (1 + (-x)^k)^((-1)^k*mu(k)/k).

E.g.f.: exp(-x*(1 + x))*g(x)^2, where g(x) = e.g.f. of A005388.

cp's OEIS Frontend

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

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