|
|
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
|
|
|
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
|
|
|
|