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A280540 G.f.: Product_{i>=1, j>=1} 1/(1 - x^(i*j))^(i*j). 11
1, 1, 5, 11, 33, 67, 180, 366, 871, 1782, 3927, 7885, 16637, 32763, 66469, 128938, 253871, 484034, 930959, 1747304, 3292730, 6092664, 11282364, 20596790, 37568653, 67736175, 121886533, 217261372, 386216073, 681119439, 1197524035, 2091091902, 3639519280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: Product_{k>=1} 1/(1 - x^k)^(k*d(k)), where d(k) = number of divisors of k (A000005). - Ilya Gutkovskiy, Aug 26 2018

log(a(n)) ~ (3/2)^(2/3) * Zeta(3)^(1/3) * log(n)^(1/3) * n^(2/3). - Vaclav Kotesovec, Aug 28 2018

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[1/(1-x^(i*j))^(i*j), {i, 1, nmax}, {j, 1, nmax}], {x, 0, nmax}], x]

nmax = 50; s = 1 - x; Do[s *= Sum[Binomial[k*DivisorSigma[0, k], j]*(-1)^j*x^(j*k), {j, 0, nmax/k}]; s = Expand[s]; s = Take[s, Min[nmax + 1, Exponent[s, x] + 1, Length[s]]]; , {k, 2, nmax}]; CoefficientList[Series[1/s, {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2018 *)

CROSSREFS

Cf. A000005, A006171, A038040, A061256, A107742, A192065, A280541.

Sequence in context: A107442 A349611 A323867 * A077917 A127864 A055936

Adjacent sequences:  A280537 A280538 A280539 * A280541 A280542 A280543

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jan 05 2017

STATUS

approved

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Last modified August 11 06:08 EDT 2022. Contains 356046 sequences. (Running on oeis4.)