A369822 Number of (undirected) Eulerian cycles in the (2n)-dipyramid graph.

372, 68880, 26310816, 17145457920, 17034981004800, 23977057921689600, 45400487332999680000, 111298452508871250739200, 342962787786595749642240000, 1297585985940925048243814400000, 5913686127296455213253427855360000, 31954282139197508581861513887744000000

Offset

2,1

Links

Andrew Howroyd, Table of n, a(n) for n = 2..100

Eric Weisstein's World of Mathematics, Dipyramidal Graph.

Eric Weisstein's World of Mathematics, Eulerian Cycle.

Formula

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

Prog

(PARI) \\ B(n, k) is A193858(n, k)
B(m, q)={sum(j=0, q, 2^(m-j) * binomial(m-j, q-j))}
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

Crossrefs

Cf. A193858.

Sequence in context: A240249 A200885 A161361 * A265659 A238774 A299832

Adjacent sequences: A369819 A369820 A369821 * A369823 A369824 A369825

Keyword

nonn

Author

Eric W. Weisstein, Feb 02 2024

Extensions

a(5) from Max Alekseyev, Feb 17 2024

a(6) onwards from Andrew Howroyd, Feb 17 2024

Status

approved