%I #22 Sep 08 2022 08:46:07
%S 0,0,1,130,2446,21146,117971,494732,1695036,4992492,13072917,31153342,
%T 68720938,142120342,278268263,519829688,932250488,1613106744,
%U 2704301673,4407716634,7005003334,10882290034,16560665275,24733398404,36310956980,52474986980,74742532605,105041888406,145801597410,200054234926,271556748751,364929262576,485814390512
%N a(n) = (5*n^9 - 30*n^7 + 63*n^5 - 50*n^3 + 12*n)/360.
%H Vincenzo Librandi, <a href="/A239094/b239094.txt">Table of n, a(n) for n = 0..1000</a>
%H C. P. Neuman and D. I. Schonbach, <a href="http://dx.doi.org/10.1137/1019006">Evaluation of sums of convolved powers using Bernoulli numbers</a>, SIAM Rev. 19 (1977), no. 1, 90--99. MR0428678 (55 #1698). See Table 1.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F G.f.: x^2*(x^6 + 120*x^5 + 1191*x^4 + 2416*x^3 + 1191*x^2 + 120*x + 1) / (x-1)^10. - _Colin Barker_, Mar 24 2014
%t Table[(5 n^9 - 30 n^7 + 63 n^5 - 50 n^3 + 12 n)/360,{n, 0, 50}] (* _Vincenzo Librandi_, Mar 24 2014 *)
%o (Magma) [(5*n^9-30*n^7+63*n^5-50*n^3+12*n)/360: n in [0..40]]; // _Vincenzo Librandi_, Mar 24 2014
%o (PARI) concat([0,0], Vec(x^2*(x^6 +120*x^5 +1191*x^4 +2416*x^3 +1191*x^2 +120*x +1) / (x -1)^10 + O(x^100))) \\ _Colin Barker_, Mar 24 2014
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_, Mar 23 2014