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%I #15 Oct 21 2022 21:25:09
%S 21,209,938,2833,6771,13881,25544,43393,69313,105441,154166,218129,
%T 300223,403593,531636,688001,876589,1101553,1367298,1678481,2040011,
%U 2457049,2935008,3479553,4096601,4792321,5573134,6445713,7416983
%N G.f.: (21+104*x+103*x^2+23*x^3+x^4)/(1-x)^5.
%C Source: the De Loera et al. article and the Haws website listed in A160747.
%H G. C. Greubel, <a href="/A160787/b160787.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = 21*n^4/2 +247*n^3/6 +147*n^2/2 +377*n/6 +21. - _R. J. Mathar_, Sep 11 2011
%F E.g.f.: (126 + 1128*x + 1623*x^2 + 625*x^3 + 63*x^4)* exp(x)/6. - _G. C. Greubel_, Apr 26 2018
%t CoefficientList[Series[(21+104x+103x^2+23x^3+x^4)/ (1-x)^5, {x,0,40}], x] (* _Harvey P. Dale_, Mar 28 2011 *)
%t LinearRecurrence[{5,-10,10,-5,1}, {21, 209, 938, 2833, 6771}, 50] (* _G. C. Greubel_, Apr 26 2018 *)
%o (PARI) for(n=0,30, print1((63*n^4 + 247*n^3 +441*n^2 + 377*n + 126)/6, ", ")) \\ _G. C. Greubel_, Apr 26 2018
%o (Magma) [(63*n^4 + 247*n^3 +441*n^2 + 377*n + 126)/6: n in [0..30]]; // _G. C. Greubel_, Apr 26 2018
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Nov 18 2009
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