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

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

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]

Crossrefs

Cf. A000203, A022629, A266891, A318416, A107742, A192065, A318483.

Sequence in context: A001216 A396891 A396199 * A079843 A290582 A346071

Adjacent sequences: A318481 A318482 A318483 * A318485 A318486 A318487

Keyword

nonn

Author

Vaclav Kotesovec, Aug 27 2018

Status

approved