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Expansion of (1+13*x+32*x^2+13*x^3+x^4)/(1-x)^5.
1

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

%S 1,18,112,403,1071,2356,4558,8037,13213,20566,30636,44023,61387,83448,

%T 110986,144841,185913,235162,293608,362331,442471,535228,641862,

%U 763693,902101,1058526,1234468,1431487,1651203,1895296,2165506,2463633,2791537

%N Expansion of (1+13*x+32*x^2+13*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="/A160765/b160765.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 G.f.: (1+13*x+32*x^2+13*x^3+x^4)/(1-x)^5.

%F a(n) = (n^2+n+1)*(5*n^2+5*n+2)/2. - _R. J. Mathar_, Sep 11 2011

%F a(n) = A000566(A002061(n+1)). - _Bruno Berselli_, Jul 31 2015

%F E.g.f.: (1/2)*(5*x^4 + 40*x^3 + 77*x^2 + 34*x + 2)*exp(x). - _G. C. Greubel_, Apr 26 2018

%t Table[(n^2 + n + 1) (5 n^2 + 5 n + 2)/2, {n, 0, 40}] (* _Bruno Berselli_, Jul 31 2015 *)

%o (Sage) [(n^2+n+1)*(5*n^2+5*n+2)/2 for n in (0..40)] # _Bruno Berselli_, Jul 31 2015

%o (Magma) [(n^2+n+1)*(5*n^2+5*n+2)/2: n in [0..40]] // _Bruno Berselli_, Jul 31 2015

%o (PARI) for(n=0,30, print1((n^2+n+1)*(5*n^2+5*n+2)/2, ", ")) \\ _G. C. Greubel_, Apr 26 2018

%Y Cf. A000566, A002061.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 18 2009