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%I #14 May 08 2017 00:29:13
%S 1,1,3,6,17,38,112,280,882,2416,8253,24458,91051,289704,1172288,
%T 3980034,17413820,62706119,294608079,1118820630,5603910081,
%U 22328924231,118432939871,492897768426,2752203529333,11918139966134,69709167028426,313080284080648,1910245872252972,8873669214476627,56283324138424814,269790676411694902
%N Expansion of Product_{k>=1} 1/(1 - x^k)^(k!!).
%C Euler transform of the double factorials (A006882).
%H Vincenzo Librandi, <a href="/A280088/b280088.txt">Table of n, a(n) for n = 0..300</a>
%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F G.f.: Product_{k>=1} 1/(1 - x^k)^(k!!).
%F a(n) ~ n!!. - _Vaclav Kotesovec_, Dec 25 2016
%t nmax = 31; CoefficientList[Series[Product[1/(1 - x^k)^(k!!), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A006882, A107895.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 25 2016
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