A005431 Embeddings of n-bouquet in sphere. (Formerly M3674)

1, 1, 4, 40, 672, 16128, 506880, 19768320, 922521600, 50185175040, 3120605429760, 218442380083200, 17004899126476800, 1457562782269440000, 136427876420419584000, 13847429456672587776000

Offset

0,3

References

Jonathan L. Gross and Thomas W. Tucker, Enumerating graph embeddings and partial-duals by genus and Euler genus, ECA 1:1 (2021) Article S2S1. See Table 1.

J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 649.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

K. Casteels and B. Stevens, Universal cycles of (n-1)-partitions of an n-set, Discr. Math., 309 (2009), 5332-5340. See Cor. 12. [From N. J. A. Sloane, Sep 15 2009]

J. L. Gross et al., Genus distributions for bouquets of circles, J. Combin. Theory, B 47 (1989), 292-306.

Formula

a(n) = 4*(2*n-3)*(n-2)*a(n-1)/n, for n > 2, the sequence shifted by 1.

a(n) = 2^n * (2*n-1)!/(n+1)!, for n > 0.

Mathematica

Join[{1}, Table[2^n(2n-1)!/(n+1)!, {n, 20}]] (* Harvey P. Dale, Oct 25 2011 *)

Prog

(Magma) [1], [2^n * Factorial(2*n-1)/Factorial(n+1): n in [1..20]]; // Vincenzo Librandi, Oct 26 2011
(PARI) concat([1], vector(20, n, 2^n*(2*n-1)!/(n+1)!))
(Sage) [1] + [2^n*factorial(2*n-1)/factorial(n+1) for n in (1..20)] # G. C. Greubel, Nov 23 2018

Crossrefs

Cf. A123828, A128850.

Sequence in context: A205671 A234294 A181088 * A153849 A372232 A251574

Adjacent sequences: A005428 A005429 A005430 * A005432 A005433 A005434

Keyword

easy,nonn,nice

Author

Simon Plouffe and N. J. A. Sloane

Extensions

Description corrected Apr 15 1998 by Wim van Dam (wimvdam(AT)mildred.physics.ox.ac.uk)

Status

approved