%I #16 Oct 13 2017 06:07:13
%S 1,123,3281,39175,286555,1508401,6271378,21836366,66220705,179784715,
%T 445824731,1025102013,2211041131,4514532465,8789910980,16416797116,
%U 29556115153,51502789451,87162399205,143684487475,231291309931,364347612673,562724586326
%N Number of magic labelings of the graph LOOP X C_10 (see comments) having magic sum n, n >= 0.
%C The graph LOOP X C_n is constructed by attaching a loop to each vertex of the cycle graph C_n.
%C The generating function for this sequence was found via the "Omega" package for Mathematica authored by Axel Riese. The package can be downloaded from the link given in the article by G. E. Andrews et al.
%H G. E. Andrews, P. Paule and A. Riese, <a href="http://www.risc.uni-linz.ac.at/research/combinat/risc/publications/#ppaule">MacMahon's partition analysis III. The Omega package</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CycleGraph.html">Cycle Graph</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Graph Loop.html">Graph Loop</a>.
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F G.f.: (1 + 112*z + 1983*z^2 + 9684*z^3 + 16120*z^4 + 9684*z^5 + 1983*z^6 + 112*z^7 + z^8)/(1 - z)^11.
%t CoefficientList[Series[(1 + 112*z + 1983*z^2 + 9684*z^3 + 16120*z^4 + 9684*z^5 + 1983*z^6 + 112*z^7 + z^8)/(1 - z)^11, {z, 0, 22}], z].
%t LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {1, 123, 3281, 39175, 286555, 1508401, 6271378, 21836366, 66220705, 179784715, 445824731}, 25] (* _Vincenzo Librandi_, Oct 12 2017 *)
%Y Cf. A293311, A293312.
%Y Cf. A000027, A000217, A019298, A006325, A244497, A244879, A244873, A244880, A293310 (magic labelings of LOOP X C_k, for k=1..9).
%K nonn
%O 0,2
%A _L. Edson Jeffery_, Oct 05 2017