A270873 a(n) = n^9 + 8*n^8 + 43*n^7 + 159*n^6 + 452*n^5 + 997*n^4 + 1725*n^3 + 2272*n^2 + 1990*n + 21.

21, 7668, 75545, 545730, 3015021, 13239896, 48243393, 151298070, 420233285, 1056651996, 2446142121, 5282430218, 10751650845, 20796493440, 38483939921, 68504620446, 117836491893, 196610583620, 319221957945, 505734798546, 783636668621, 1190003472168

Offset

0,1

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, 9th row).

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

G.f.: (21+7458*x-190*x^2+132820*x^3+41496*x^4+187124*x^5-30698*x^6+30660*x^7-6565*x^8+754*x^9)/(1-x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10).

Mathematica

Table[n^9 + 8 n^8 + 43 n^7 + 159 n^6 + 452 n^5 + 997 n^4 + 1725 n^3 + 2272 n^2 + 1990 n + 21, {n, 0, 40}]
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {21, 7668, 75545, 545730, 3015021, 13239896, 48243393, 151298070, 420233285, 1056651996}, 30] (* Harvey P. Dale, Dec 02 2018 *)

Prog

(Magma) [n^9+8*n^8+43*n^7+159*n^6+452*n^5+997*n^4+1725*n^3+2272*n^2+1990*n
+21: n in [0..40]]:
(PARI) x='x+O('x^99); Vec((21+7458*x-190*x^2+132820*x^3+41496*x^4+187124*x^5-30698*x^6+30660*x^7-6565*x^8+754*x^9)/(1-x)^10) \\ Altug Alkan, Apr 04 2016

Crossrefs

Cf. A270867, A270868, A270869, A270870, A270871, A270872.

Sequence in context: A231906 A250063 A307931 * A263278 A176446 A135823

Adjacent sequences: A270870 A270871 A270872 * A270874 A270875 A270876

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 04 2016

Status

approved