A162726 - OEIS

%I #18 Sep 08 2022 08:45:46

%S 1,27,378,3653,27378,169533,902537,4244616,17985915,69697614,

%T 249887403,836666037,2635961496,7863966540,22333781484,60654192289,

%U 158133109329,397109727144,963390950574,2263730057379,5163854598459,11458797521755

%N G.f. is the polynomial (Product_{k=1..27} (1 - x^(3*k)))/(1-x)^27.

%C This is a row of the triangle in A162499. Only finitely many terms are nonzero.

%H G. C. Greubel, <a href="/A162726/b162726.txt">Table of n, a(n) for n = 0..1107</a>

%p m:=27: seq(coeff(series(mul((1-x^(3*k)),k=1..m)/(1-x)^m, x,n+1),x,n),n=0..21); # _Muniru A Asiru_, Jul 08 2018

%t With[{num=Times@@(1-x^(3*Range[27]))},CoefficientList[Series[num/(1-x)^27,{x,0,30}],x]] _Harvey P. Dale_, May 20 2012

%o (PARI) x='x+O('x^50); A = prod(k=1, 27, (1-x^(3*k)))/(1-x)^27; Vec(A) \\ _G. C. Greubel_, Jul 06 2018

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); F:=(&*[(1-x^(3*k)): k in [1..27]])/(1-x)^27; Coefficients(R!(F)); // _G. C. Greubel_, Jul 06 2018

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Dec 02 2009