A327799 Expansion of 1 / (1 + Sum_{i>=1} Sum_{j=1..i} x^(i*j)).

1, -1, 0, 0, -1, 2, -2, 2, -1, -2, 5, -6, 5, -1, -5, 10, -14, 14, -5, -10, 26, -38, 36, -15, -20, 60, -91, 93, -51, -33, 138, -223, 237, -145, -52, 307, -528, 596, -412, -43, 674, -1258, 1492, -1126, 84, 1442, -2938, 3687, -3034, 680, 3000, -6818, 9050, -7997

Offset

0,6

Links

Table of n, a(n) for n=0..53.

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).

Mathematica

nmax = 53; 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, 53}]

Crossrefs

Cf. A038548, A159933, A327739.

Sequence in context: A271205 A303841 A093116 * A198199 A366039 A124369

Adjacent sequences: A327796 A327797 A327798 * A327800 A327801 A327802

Keyword

sign

Author

Ilya Gutkovskiy, Sep 25 2019

Status

approved