A327746 Expansion of Product_{i>=1, j>=1} 1 / (1 + (-x)^(i*(2*j - 1))).

1, 1, 0, 2, 2, 2, 3, 3, 6, 7, 8, 9, 14, 16, 17, 26, 30, 35, 43, 52, 62, 77, 87, 104, 133, 152, 173, 212, 251, 287, 344, 397, 465, 549, 627, 729, 864, 986, 1127, 1325, 1524, 1740, 2009, 2306, 2641, 3047, 3455, 3942, 4549, 5157, 5846, 6700, 7605, 8608

Offset: 0

Author

Ilya Gutkovskiy, Sep 23 2019

Keywords

• nonn

Links

• Jason Bard, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A001227, A107742, A288007, A327731.

Programs

Mathematica

nmax = 53; CoefficientList[Series[Product[1/(1 + (-x)^k)^DivisorSum[k, Mod[#, 2] &], {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[(-1)^k Sum[(-1)^(k/d) d DivisorSum[d, Mod[#, 2] &], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 53}]

Formula

G.f.: Product_{k>=1} 1 / (1 + (-x)^k)^A001227(k).