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%I #14 Sep 23 2017 15:45:03
%S 1,6,22,63,155,343,702,1352,2480,4370,7445,12323,19894,31421,48675,
%T 74111,111099,164221,239656,345670,493243,696861,975518,1353971,
%U 1864315,2547941,3457972,4662273,6247169,8322010,11024775,14528914,19051697
%N Apply partial sum operator 5 times to partition numbers.
%C In general, if g.f. = 1/(1-x)^m * Product_{k>=1} 1/(1-x^k), then a(n) ~ 2^(m/2 - 2) * 3^((m-1)/2) * n^(m/2 - 1) * exp(Pi*sqrt(2*n/3)) / Pi^m. - _Vaclav Kotesovec_, Oct 30 2015
%H Vaclav Kotesovec, <a href="/A120477/b120477.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: 1/((1-x)^5*Product_{k>=1} (1-x^k)). - _Emeric Deutsch_, Jul 24 2006
%F a(n) ~ 9*sqrt(2)*n^(3/2) * exp(Pi*sqrt(2*n/3)) / Pi^5. - _Vaclav Kotesovec_, Oct 30 2015
%p with(combinat): g:=1/(1-x)^5/product(1-x^k,k=1..50): gser:=series(g,x=0,40): seq(coeff(gser,x,n),n=0..37); # _Emeric Deutsch_, Jul 24 2006
%t nmax = 50; CoefficientList[Series[1/((1-x)^5 * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 30 2015 *)
%Y Cf. A000041, A000070, A014153, A014160, A014161.
%Y Column k=6 of A292508.
%K nonn
%O 0,2
%A _Jonathan Vos Post_, Jul 21 2006
%E More terms from _Emeric Deutsch_, Jul 24 2006
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