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%I #39 Mar 23 2024 08:16:33
%S 1,17,145,833,3649,13073,40081,108545,265729,598417,1256465,2485825,
%T 4673345,8405905,14546705,24331777,39490049,62390545,96220561,
%U 145198913,214828609,312193553,446304145,628496897,872893441,1196924561,1621925137,2173806145,2883810113,3789356689,4934985233
%N Crystal ball sequence for 8-dimensional cubic lattice.
%C This is row/column 8 of the Delannoy numbers array, A008288, which is the main entry for these numbers, listing many more properties. - _Shel Kaphan_, Jan 06 2023
%H T. D. Noe, <a href="/A008417/b008417.txt">Table of n, a(n) for n = 0..1000</a>
%H J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).
%H <a href="/index/Cor#crystal_ball">Index entries for crystal ball sequences</a>
%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 G.f.: (1+x)^8/(1-x)^9.
%F First differences of A099196. - _Alexander Adamchuk_, May 23 2006
%F a(n) = (2*n^8 + 8*n^7 + 84*n^6 + 224*n^5 + 798*n^4 + 1232*n^3 + 1636*n^2 + 1056*n + 315)/315. - _Alexander Adamchuk_, May 23 2006
%F Sum_{n >= 1} (-1)^(n+1)/(n*a(n-1)*a(n)) = log(2) - (1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8). - _Peter Bala_, Mar 23 2024
%t CoefficientList[Series[-(z + 1)^8/(z - 1)^9, {z, 0, 200}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jun 19 2011 *)
%Y Cf. A001849, A099196.
%Y Partial sums of A008416.
%Y Cf. A240876.
%Y Row/Column 8 of A008288.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Alexander Adamchuk_, May 23 2006
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