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%I #14 Jun 13 2015 00:52:34
%S 0,35,1430,13941,75205,289800,897165,2379300,5620846,12135825,
%T 24377000,46145495,83119995,143526526,238971495,385462350,604641900,
%U 925264015,1384940106,2032187465,2928812225,4152661380,5800779985,7993011336,10876079610,14628196125
%N (n^8 - 60*n^6 + 90*n^5 + 1160*n^4 - 3204*n^3 - 5349*n^2 + 26586*n - 23760)/24.
%H Chai Wah Wu, <a href="/A135923/b135923.txt">Table of n, a(n) for n = 3..1000</a>
%H Ellingsrud, Geir and Stromme, Stein Arild, <a href="http://arxiv.org/abs/alg-geom/9411005">Bott's formula and enumerative geometry</a>, J. Amer. Math. Soc. 9 (1996), 175-193. [arXiv:alg-geom/9411005]
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F a(n) = (n-3)*(n+6)*(n^6-3*n^5-33*n^4+135*n^3+161*n^2-1257*n+1320)/24 .
%F a(n)=9*a(n-1)-36*a(n-2)+ 84*a(n-3)-126*a(n-4)+126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9), n>=12 [_Harvey P. Dale_, Oct 20 2011]
%F G.f.: x^4*(-10*x^7 +279*x^6 -1071*x^5 +879*x^4 +1724*x^3 -2331*x^2 -1115*x - 35)/(x-1)^9 [_Harvey P. Dale_, Oct 20 2011]
%t Table[(n^8-60n^6+90n^5+1160n^4-3204n^3-5349n^2+26586n-23760)/24, {n,3,30}] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,35,1430,13941,75205,289800,897165,2379300,5620846},30] (* _Harvey P. Dale_, Oct 20 2011 *)
%o (Python)
%o from itertools import islice
%o def A135923_generator():
%o ....m = [1680, -840, -1380, -240, 641, 393, -209, -10, 0]
%o ....yield m[-1]
%o ....while True:
%o ........for i in range(8):
%o ............m[i+1]+= m[i]
%o ........yield m[-1]
%o list(islice(A135923_generator(),0,50,1)) # _Chai Wah Wu_, Nov 14 2014
%K nonn
%O 3,2
%A _N. J. A. Sloane_, Mar 07 2008
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