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A327727 Expansion of Product_{i>=1, j>=0}  (1 + x^(i*2^j)) / (1 - x^(i*2^j)). 0
1, 2, 6, 12, 28, 52, 104, 184, 340, 578, 1004, 1652, 2752, 4404, 7088, 11080, 17362, 26592, 40730, 61284, 92096, 136408, 201608, 294456, 428952, 618658, 889684, 1268624, 1803520, 2545164, 3580784, 5005584, 6976046, 9667164, 13356364, 18360368, 25165732 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of the sequences A000041 and A092119.

LINKS

Table of n, a(n) for n=0..36.

FORMULA

G.f.: Product_{k>=1} ((1 + x^k) / (1 - x^k))^A001511(k).

G.f.: Product_{k>=1} 1 / (1 - x^k)^(A001511(k) + 1).

MATHEMATICA

nmax = 36; CoefficientList[Series[Product[1/(1 - x^k)^(IntegerExponent[2 k, 2] + 1), {k, 1, nmax}], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (IntegerExponent[2 d, 2] + 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 36}]

PROG

(PARI) seq(n)={Vec(1/prod(k=1, n, (1 - x^k + O(x*x^n))^(2+valuation(k, 2))))} \\ Andrew Howroyd, Sep 23 2019

CROSSREFS

Cf. A000041, A001511, A085058, A092119, A170925.

Sequence in context: A290674 A290419 A159553 * A222970 A112510 A284449

Adjacent sequences:  A327724 A327725 A327726 * A327728 A327729 A327730

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 23 2019

STATUS

approved

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Last modified September 26 03:40 EDT 2022. Contains 356986 sequences. (Running on oeis4.)