A307923 Number of (undirected) Hamiltonian cycles in the n-cocktail party graph.

0, 1, 16, 744, 56256, 6385920, 1018114560, 217234805760, 59809766768640, 20651520261980160, 8740913386202726400, 4451168534087349043200, 2685007039858238501683200, 1893459488121880710532300800, 1543515756205349079583241011200, 1440363330182802737753009160192000

Offset

1,3

Links

Table of n, a(n) for n=1..16.

Eric Weisstein's World of Mathematics, Cocktail Party Graph

Eric Weisstein's World of Mathematics, Hamiltonian Cycle

Formula

a(n) = A129348(n)/2.

Mathematica

Join[{0}, Table[Gamma[2 n] Hypergeometric1F1[-n, 1 - 2 n, -2]/2, {n, 2, 20}]] (* Eric W. Weisstein, Feb 20 2025 *)
Join[{0}, RecurrenceTable[{-4 (1 + n) (2 + n) (5 + 2 n) a[n] - 2 (2 + n) (17 + 16 n + 4 n^2) a[n + 1] + (3 + 2 n) a[n + 2] == 0, a[1] == 1, a[2] == 16}, a[n], {n, 20}]] (* Eric W. Weisstein, Feb 20 2025 *)

Crossrefs

Cf. A129348, A167987, A307935.

Sequence in context: A086701 A218297 A339202 * A159375 A221527 A129008

Adjacent sequences: A307920 A307921 A307922 * A307924 A307925 A307926

Keyword

nonn

Author

Eric W. Weisstein, May 06 2019

Status

approved