A318484 Expansion of Product_{k>=1} (1 + k*x^k)^sigma(k), where sigma = A000203.
1, 1, 6, 18, 52, 142, 404, 1018, 2624, 6645, 16124, 38857, 92245, 214841, 494098, 1125062, 2522188, 5604930, 12327860, 26838595, 57913194, 123951482, 263019720, 553989989, 1158449522, 2405179547, 4961047246, 10168544537, 20714279168, 41952595411, 84494479578
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
Programs
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Mathematica
nmax = 40; CoefficientList[Series[Product[(1+k*x^k)^DivisorSigma[1, k], {k, 1, nmax}], {x, 0, nmax}], x] nmax = 40; s = 1 + x; Do[s *= Sum[Binomial[DivisorSigma[1, k], j]*k^j*x^(j*k), {j, 0, nmax/k}]; s = Expand[s]; s = Take[s, Min[nmax + 1, Exponent[s, x] + 1, Length[s]]];, {k, 2, nmax}]; CoefficientList[s, x]