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 A005431 Embeddings of n-bouquet in sphere. (Formerly M3674) 2
 1, 1, 4, 40, 672, 16128, 506880, 19768320, 922521600, 50185175040, 3120605429760, 218442380083200, 17004899126476800, 1457562782269440000, 136427876420419584000, 13847429456672587776000 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 14 22:40 EDT 2024. Contains 375167 sequences. (Running on oeis4.)