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G.f. is the polynomial (Product_{k=1..14} (1 - x^(3*k)))/(1-x)^14.
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%I #14 Sep 08 2022 08:45:46

%S 1,14,105,559,2366,8463,26571,75126,194817,469728,1064166,2284086,

%T 4675748,9179014,17358666,31744441,56319263,97205511,163611175,

%U 269111465,433356858,684315658,1061177819,1618066905,2428728445

%N G.f. is the polynomial (Product_{k=1..14} (1 - x^(3*k)))/(1-x)^14.

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

%H G. C. Greubel, <a href="/A162632/b162632.txt">Table of n, a(n) for n = 0..301</a>

%p m:=14: seq(coeff(series(mul((1-x^(3*k)),k=1..m)/(1-x)^m, x,n+1),x,n),n=0..24); # _Muniru A Asiru_, Jul 07 2018

%t CoefficientList[Series[(Times@@(1-x^(3*Range[14])))/(1-x)^14,{x,0,30}],x] (* _Harvey P. Dale_, Apr 28 2018 *)

%o (PARI) x='x+O('x^50); A = prod(k=1, 14, (1-x^(3*k)))/(1-x)^14; 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..14]])/(1-x)^14; Coefficients(R!(F)); // _G. C. Greubel_, Jul 06 2018

%K nonn

%O 0,2

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