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%I #18 Feb 18 2024 13:39:57
%S 372,68880,26310816,17145457920,17034981004800,23977057921689600,
%T 45400487332999680000,111298452508871250739200,
%U 342962787786595749642240000,1297585985940925048243814400000,5913686127296455213253427855360000,31954282139197508581861513887744000000
%N Number of (undirected) Eulerian cycles in the (2n)-dipyramid graph.
%H Andrew Howroyd, <a href="/A369822/b369822.txt">Table of n, a(n) for n = 2..100</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DipyramidalGraph.html">Dipyramidal Graph</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EulerianCycle.html">Eulerian Cycle</a>.
%F a(n) = n!*(n-1)!*(2^(2*n)*Sum_{k=0..n} binomial(2*n, 2*k)*binomial(2*k, k) - binomial(2*n, n) - 4*Sum_{q=0..2*n-2} binomial(q, floor(q/2)) * A193858(2*n-2, q)). - _Andrew Howroyd_, Feb 18 2024
%o (PARI) \\ B(n,k) is A193858(n,k)
%o B(m,q)={sum(j=0, q, 2^(m-j) * binomial(m-j,q-j))}
%o a(n)={n!*(n-1)!*(2^(2*n)*sum(k=0, n, binomial(2*n, 2*k)*binomial(2*k, k)) - binomial(2*n, n) - 4*sum(q=0, 2*n-2, binomial(q, q\2) * B(2*n-2, q)))} \\ _Andrew Howroyd_, Feb 18 2024
%Y Cf. A193858.
%K nonn
%O 2,1
%A _Eric W. Weisstein_, Feb 02 2024
%E a(5) from _Max Alekseyev_, Feb 17 2024
%E a(6) onwards from _Andrew Howroyd_, Feb 17 2024
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