OFFSET
0,3
COMMENTS
Invert transform of A007862.
FORMULA
G.f.: 1 / (1 - Sum_{k>=1} x^(k*(k + 1)/2) / (1 - x^(k*(k + 1)/2))).
a(0) = 1; a(n) = Sum_{k=1..n} A007862(k) * a(n-k).
MATHEMATICA
nmax = 33; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1)/2)/(1 - x^(k (k + 1)/2)), {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Length[Select[Divisors[k], IntegerQ[Sqrt[8 # + 1]] &]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 33}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 24 2019
STATUS
approved