A318968 Expansion of exp(Sum_{k>=1} ( Sum_{d|k, d odd} d^k ) * x^k/k).
1, 1, 1, 10, 10, 635, 797, 118446, 124071, 43174194, 45404910, 25982930761, 26443958420, 23324558686914, 23640266984002, 29216576615057082, 29447535265299613, 48690644491136860817, 48980258924147884960, 104176334607664412086539, 104636388540330684649083, 278323070872780066332365486
Offset: 0
Keywords
Programs
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Mathematica
nmax = 21; CoefficientList[Series[Exp[Sum[Sum[Mod[d, 2] d^k, {d, Divisors[k]}] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] nmax = 21; CoefficientList[Series[Product[1/(1 - (2 k - 1)^(2 k - 1) x^(2 k - 1))^(1/(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] a[n_] := a[n] = If[n == 0, 1, Sum[Sum[Mod[d, 2] d^k, {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 21}]
Formula
G.f.: Product_{k>=1} 1/(1 - (2*k - 1)^(2*k-1)*x^(2*k-1))^(1/(2*k-1)).