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A327739 Expansion of 1 / (1 - Sum_{i>=1} Sum_{j=1..i} x^(i*j)). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Invert transform of A038548.

LINKS

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

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).

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}]

CROSSREFS

Cf. A038548, A129921, A182269, A211856.

Sequence in context: A327738 A215253 A079580 * A018000 A329668 A320222

Adjacent sequences:  A327736 A327737 A327738 * A327740 A327741 A327742

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 23 2019

STATUS

approved

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Last modified June 4 07:43 EDT 2020. Contains 334822 sequences. (Running on oeis4.)