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%I #16 Sep 08 2022 08:45:11
%S 1,5,15,39,90,189,375,707,1276,2226,3768,6210,10002,15780,24432,37198,
%T 55772,82443,120300,173445,247284,348916,487555,675088,926784,1262091,
%U 1705644,2288518,3049654,4037611,5312713,6949490,9039627,11695524,15054338,19282807
%N Number of triangular partitions of n of order 5.
%H Vincenzo Librandi, <a href="/A084447/b084447.txt">Table of n, a(n) for n = 0..1000</a>
%H G. Almkvist, <a href="https://projecteuclid.org/euclid.em/1047674152">Asymptotic formulas and generalized Dedekind sums</a>, Exper. Math., 7 (No. 4, 1998), pp. 343-359.
%F G.f.: 1/((1-x)^5*(1-x^3)^4*(1-x^5)^3*(1-x^7)^2*(1-x^9)).
%t CoefficientList[Series[1/((1 - x)^5 (1 - x^3)^4 (1 - x^5)^3 (1 - x^7)^2 (1 - x^9)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Aug 29 2016 *)
%o (PARI) Vec( 1/((1-x)^5*(1-x^3)^4*(1-x^5)^3*(1-x^7)^2*(1-x^9)) + O(x^50)) \\ _Michel Marcus_, Dec 08 2014
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^5*(1-x^3)^4*(1-x^5)^3*(1-x^7)^2*(1-x^9)))); // _Vincenzo Librandi_, Aug 29 2016
%Y Cf. A001840, A084439, A084446.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jun 27 2003
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