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%I M4671 N1998 #47 Apr 13 2022 13:25:16
%S 0,9,259,1974,8778,28743,77077,179452,375972,725781,1312311,2249170,
%T 3686670,5818995,8892009,13211704,19153288,27170913,37808043,51708462,
%U 69627922,92446431,121181181,157000116,201236140,255401965,321205599,400566474,495632214
%N Central factorial numbers: column 2 in triangle A008956.
%D J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A001823/b001823.txt">Table of n, a(n) for n = 1..1000</a>
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F a(n) = n*(n-1)*(2*n+1)*(2*n-1)*(2*n-3)*(10*n+7)/90.
%F If we replace n with n-1/2 in this formula we get 16*A000586(n).
%F G.f.: z*(9+196*z+350*z**2+84*z**3+z**4)/(1-z)^7.
%F a(1)=0, a(2)=9, a(3)=259, a(4)=1974, a(5)=8778, a(6)=28743, a(7)=77077, 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). - _Harvey P. Dale_, Jun 09 2013
%p A001823:=-(9+196*z+350*z**2+84*z**3+z**4)/(z-1)**7; # conjectured (correctly) by _Simon Plouffe_ in his 1992 dissertation
%t Table[1/90*n*(n - 1)*(2*n + 1)*(2*n - 1)*(2*n - 3)*(10*n + 7), {n, 40}] (* _Stefan Steinerberger_, Apr 15 2006 *)
%t LinearRecurrence[{7,-21,35,-35,21,-7,1}, {0,9,259,1974,8778,28743,77077},30] (* _Harvey P. Dale_, Jun 09 2013 *)
%Y A bisection of A181888.
%Y Column 2 in triangle A008956.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _Stefan Steinerberger_, Apr 15 2006