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
KEYWORD
easy,nonn,nice
AUTHOR
EXTENSIONS
Description corrected Apr 15 1998 by Wim van Dam (wimvdam(AT)mildred.physics.ox.ac.uk)
STATUS
approved