A270870 a(n) = n^6 + 5*n^5 + 19*n^4 + 44*n^3 + 72*n^2 + 69*n + 5.
5, 215, 1311, 5531, 18329, 50775, 122675, 266411, 531501, 989879, 1741895, 2923035, 4711361, 7335671, 11084379, 16315115, 23465045, 33061911, 45735791, 62231579, 83422185, 110322455, 144103811, 186109611, 237871229, 301124855, 377829015, 470182811
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Andrew Misseldine, Counting Schur Rings over Cyclic Groups, arXiv preprint arXiv:1508.03757 [math.RA], 2015. (page 19, 4th row; page 21, 6th row).
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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Magma
[n^6+5*n^5+19*n^4+44*n^3+72*n^2+69*n+5: n in [0..40]];
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Mathematica
Table[n^6 + 5 n^5 + 19 n^4 + 44 n^3 + 72 n^2 + 69 n + 5, {n, 0, 40}] -
PARI
x='x+O('x^99); Vec((5+180*x-89*x^2+694*x^3-207*x^4+158*x^5-21*x^6)/(1-x)^7) \\ Altug Alkan, Apr 03 2016
Formula
O.g.f.: (5 +180*x -89*x^2 +694*x^3 -207*x^4 +158*x^5 -21*x^6)/(1-x)^7.
E.g.f.: (5 +210*x +443*x^2 +373*x^3 +134*x^4 +20*x^5 +x^6)*exp(x).
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).