%I #27 Sep 08 2022 08:45:11
%S 1,244,8020,108020,867395,4951496,22161864,82628040,267156165,
%T 770440540,2022773116,4909947484,11150268935,23913084560,48796284560,
%U 95322158736,179163294729,325374464580,572984364580,981394464580,1639143014731,2675722491224,4277290592600
%N a(n) = Sum_{i=1..n} binomial(i+1,2)^5.
%D Elisabeth Busser and Gilles Cohen, Neuro-Logies - "Chercher, jouer, trouver", La Recherche, April 1999, No. 319, page 97.
%H T. D. Noe, <a href="/A085440/b085440.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F a(n) = (113400*n^11 +1247400*n^10 +5544000*n^9 +12474000*n^8 +14196600*n^7 +6237000*n^6 -831600*n^5 +1108800*n^3 -172800*n)/11!.
%F G.f.: x*(x^8+232*x^7+5158*x^6+27664*x^5+47290*x^4+27664*x^3+5158*x^2+232*x+1) / (x-1)^12. - _Colin Barker_, May 02 2014
%t Table[(113400*n^11 +1247400*n^10 +5544000*n^9 +12474000*n^8 +14196600*n^7 +6237000*n^6 -831600*n^5 +1108800*n^3 -172800*n)/11!, {n,1,50}] (* _G. C. Greubel_, Nov 22 2017 *)
%o (PARI) for(n=1,30, print1(sum(k=1,n, binomial(k+1,2)^5), ", ")) \\ _G. C. Greubel_, Nov 22 2017
%o (Magma) [(113400*n^11 +1247400*n^10 +5544000*n^9 +12474000*n^8 +14196600*n^7 +6237000*n^6 -831600*n^5 +1108800*n^3 -172800*n )/Factorial(11): n in [1..30]]; // _G. C. Greubel_, Nov 22 2017
%Y Column k=5 of A334781.
%Y Cf. A000292, A087127, A024166, A024166, A085438, A085439, A085441, A085442, A000332, A086020, A086021, A086022, A000389, A086023, A086024, A000579, A086025, A086026, A000580, A086027, A086028, A027555, A086029, A086030.
%K easy,nonn
%O 1,2
%A _André F. Labossière_, Jun 30 2003
%E Formula edited by _Colin Barker_, May 02 2014