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A270870 a(n) = n^6 + 5*n^5 + 19*n^4 + 44*n^3 + 72*n^2 + 69*n + 5.

%I A270870 #12 Sep 08 2022 08:46:16
%S A270870 5,215,1311,5531,18329,50775,122675,266411,531501,989879,1741895,
%T A270870 2923035,4711361,7335671,11084379,16315115,23465045,33061911,45735791,
%U A270870 62231579,83422185,110322455,144103811,186109611,237871229,301124855,377829015,470182811
%N A270870 a(n) = n^6 + 5*n^5 + 19*n^4 + 44*n^3 + 72*n^2 + 69*n + 5.
%H A270870 Vincenzo Librandi, <a href="/A270870/b270870.txt">Table of n, a(n) for n = 0..1000</a>
%H A270870 Andrew Misseldine, <a href="http://arxiv.org/abs/1508.03757">Counting Schur Rings over Cyclic Groups</a>, arXiv preprint arXiv:1508.03757 [math.RA], 2015. (page 19, 4th row; page 21, 6th row).
%H A270870 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A270870 O.g.f.: (5 +180*x -89*x^2 +694*x^3 -207*x^4 +158*x^5 -21*x^6)/(1-x)^7.
%F A270870 E.g.f.: (5 +210*x +443*x^2 +373*x^3 +134*x^4 +20*x^5 +x^6)*exp(x).
%F A270870 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).
%t A270870 Table[n^6 + 5 n^5 + 19 n^4 + 44 n^3 + 72 n^2 + 69 n + 5, {n, 0, 40}]
%o A270870 (Magma) [n^6+5*n^5+19*n^4+44*n^3+72*n^2+69*n+5: n in [0..40]];
%o A270870 (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
%Y A270870 Cf. A270867, A270868, A270869.
%K A270870 nonn,easy
%O A270870 0,1
%A A270870 _Vincenzo Librandi_, Apr 03 2016