A239094 a(n) = (5*n^9 - 30*n^7 + 63*n^5 - 50*n^3 + 12*n)/360.
0, 0, 1, 130, 2446, 21146, 117971, 494732, 1695036, 4992492, 13072917, 31153342, 68720938, 142120342, 278268263, 519829688, 932250488, 1613106744, 2704301673, 4407716634, 7005003334, 10882290034, 16560665275, 24733398404, 36310956980, 52474986980, 74742532605, 105041888406, 145801597410, 200054234926, 271556748751, 364929262576, 485814390512
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- C. P. Neuman and D. I. Schonbach, Evaluation of sums of convolved powers using Bernoulli numbers, SIAM Rev. 19 (1977), no. 1, 90--99. MR0428678 (55 #1698). See Table 1.
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
Programs
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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
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Mathematica
Table[(5 n^9 - 30 n^7 + 63 n^5 - 50 n^3 + 12 n)/360,{n, 0, 50}] (* Vincenzo Librandi, Mar 24 2014 *) -
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
Formula
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