A327747 Expansion of Product_{i>=1, j>=1} 1 / (1 + (-x)^(i*j^2)).

1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 1, 1, 0, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 3, 4, 3, 4, 4, 1, 4, 3, 4, 7, 6, 7, 6, 4, 5, 5, 7, 9, 9, 9, 8, 7, 7, 7, 10, 14, 13, 12, 14, 10, 12, 16, 13, 20, 19, 20, 20, 16, 18, 20, 22, 26, 27, 27, 28, 23, 26, 25, 31, 38, 36, 40

Offset

0,10

Links

Table of n, a(n) for n=0..75.

Formula

G.f.: Product_{k>=1} 1 / (1 + (-x)^k)^A046951(k).

Mathematica

nmax = 75; CoefficientList[Series[Product[1/(1 + (-x)^k)^Length[Select[Divisors[k], IntegerQ[Sqrt[#]] &]], {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[(-1)^k Sum[(-1)^(k/d) d Length[Select[Divisors[d], IntegerQ[Sqrt[#]] &]], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 75}]

Crossrefs

Cf. A004101, A046951, A280451.

Sequence in context: A317950 A255212 A323011 * A282750 A265890 A226920

Adjacent sequences: A327744 A327745 A327746 * A327748 A327749 A327750

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 23 2019

Status

approved