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%I #30 Feb 03 2022 02:30:19
%S 1,241,26641,338401,2240161,10242001,36638641,109907521,288653761,
%T 683158321,1486914001,3020862241,5793372001,10579330321,18522042481,
%U 31261968001,51096647041,81176500081,125741512081,190404140641,282484116001,411401129041,589131731761
%N Number of points in interior of n-th crystal ball in E_8 lattice.
%H Vincenzo Librandi, <a href="/A001361/b001361.txt">Table of n, a(n) for n = 1..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 G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/E8.html">Home page for this lattice</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.: -x*(x^8 + 232*x^7 + 7228*x^6 + 55384*x^5 + 133510*x^4 + 107224*x^3 + 24508*x^2 + 232*x + 1)/(x - 1)^9. - _Colin Barker_, Oct 29 2012
%p a:= n-> 57/7*n^8-108/7*n^7+30*n^6-72*n^5+39*n^4-36*n^3+300/7*n^2+24/7*n+1:
%p seq (a(n), n=1..30);
%t CoefficientList[Series[-(x^8 + 232 x^7 + 7228 x^6 + 55384 x^5 + 133510 x^4 + 107224 x^3 + 24508 x^2 + 232 x + 1)/(x - 1)^9, {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 13 2013 *)
%Y Cf. A008340, A008349.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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