A327739 Expansion of 1 / (1 - Sum_{i>=1} Sum_{j=1..i} x^(i*j)).

1, 1, 2, 4, 9, 18, 38, 78, 163, 338, 703, 1458, 3031, 6293, 13073, 27150, 56396, 117130, 243289, 505310, 1049552, 2179938, 4527804, 9404355, 19533126, 40570816, 84266725, 175024267, 363530253, 755062265, 1568285122, 3257371187, 6765649491, 14052439669

Offset: 0

Author

Ilya Gutkovskiy, Sep 23 2019

Keywords

• nonn

Comments

Invert transform of A038548.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A038548, A129921, A182269, A211856.

Programs

Maple

a:= proc(n) option remember; `if`(n<1, 1, add(a(n-i)*
      ceil(numtheory[sigma][0](i)/2), i=1..n))
    end:
seq(a(n), n=0..34);  # Alois P. Heinz, Sep 23 2019

Mathematica

nmax = 33; CoefficientList[Series[1/(1 - Sum[x^(k^2)/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Floor[(DivisorSigma[0, k] + 1)/2] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 33}]

Formula

G.f.: 1 / (1 - Sum_{k>=1} x^(k^2) / (1 - x^k)).

a(0) = 1; a(n) = Sum_{k=1..n} A038548(k) * a(n-k).