A084446 - OEIS

%I #14 Sep 08 2022 08:45:11

%S 1,4,10,23,47,88,158,270,443,706,1094,1654,2450,3561,5087,7159,9936,

%T 13613,18437,24702,32764,43060,56103,72505,92999,118439,149828,188346,

%U 235356,292437,361424,444417,543822,662405,803304,970085,1166807,1398040,1668939

%N Number of triangular partitions of n of order 4.

%H Vincenzo Librandi, <a href="/A084446/b084446.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)^4*(1-x^3)^3*(1-x^5)^2*(1-x^7)).

%t CoefficientList[Series[1/((1 - x)^4 (1-x^3)^3 (1-x^5)^2 (1 - x^7)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 29 2016 *)

%o (PARI) Vec(1/((1-x)^4*(1-x^3)^3*(1-x^5)^2*(1-x^7)) + O(x^50)) \\ _Michel Marcus_, Dec 08 2014

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^4*(1-x^3)^3*(1-x^5)^2*(1-x^7)))); // _Vincenzo Librandi_, Aug 29 2016

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jun 27 2003