A239095 a(n) = (n^7 - 21*n^3 + 20*n)/210.
0, 0, 0, 8, 72, 360, 1312, 3888, 9936, 22704, 47520, 92664, 170456, 298584, 501696, 813280, 1277856, 1953504, 2914752, 4255848, 6094440, 8575688, 11876832, 16212240, 21838960, 29062800, 38244960, 49809240, 64249848, 82139832, 104140160, 131009472, 163614528, 202941376, 250107264, 306373320, 373158024, 452051496, 544830624, 653475056, 780184080
Offset: 0
Keywords
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 3.
- Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
Programs
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Magma
[(n^7-21*n^3+20*n)/210: n in [0..40]]; // Vincenzo Librandi, Mar 24 2014
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Mathematica
Table[(n^7 - 21 n^3 + 20 n)/210, {n, 0, 50}] (* Vincenzo Librandi, Mar 24 2014 *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,0,0,8,72,360,1312,3888},50] (* Harvey P. Dale, Apr 26 2018 *)
Formula
G.f.: 8*x^3*(1 + x + x^2)/(1 - x)^8. - Ilya Gutkovskiy, Feb 24 2017