A162581 G.f.: A(x) = exp( 2*Sum_{n>=1} A006519(n)^2 * x^n/n ), where A006519(n) = highest power of 2 dividing n.
1, 2, 6, 10, 26, 42, 86, 130, 258, 386, 694, 1002, 1754, 2506, 4134, 5762, 9346, 12930, 20198, 27466, 42330, 57194, 85750, 114306, 169602, 224898, 326934, 428970, 618138, 807306, 1144390, 1481474, 2084610, 2687746, 3732422, 4777098, 6591386
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + 2*x + 6*x^2 + 10*x^3 + 26*x^4 + 42*x^5 + 86*x^6 + ... log(A(x))/2 = 2^0*x + 2^2*x^2 + 2^0*x^3/3 + 2^4*x^4/4 + 2^0*x^5/5 + 2^2*x^6/6 + 2^0*x^7/7 + 2^6*x^8/8 + ... + A006519(n)^2*x^n/n + ...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
nmax = 200; a[n_]:= SeriesCoefficient[Series[Exp[ Sum[2^(2*IntegerExponent[k, 2] + 1)*q^k/k, {k, 1, nmax}]], {q,0,nmax}], n]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jul 04 2018 *) -
PARI
{a(n)=local(L=sum(m=1,n,2*(2^valuation(m,2))^2*x^m/m)+x*O(x^n));polcoeff(exp(L),n)}