OFFSET
0,4
COMMENTS
Weigh transform of A007862.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: Product_{k>=1} (1 + x^k)^A007862(k).
MATHEMATICA
nmax = 48; CoefficientList[Series[Product[(1 + x^k)^Length[Select[Divisors[k], IntegerQ[Sqrt[8 # + 1]] &]], {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d Length[Select[Divisors[d], IntegerQ[Sqrt[8 # + 1]] &]], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 48}]
nmax = 50; CoefficientList[Series[Product[QPochhammer[-1, x^(k*(k + 1)/2)]/2, {k, 1, Sqrt[2*nmax]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 24 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 23 2019
STATUS
approved