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Search: id:A002011
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| A002011 |
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4*(2n+1)!/n!^2.
(Formerly M3598 N1458)
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+0
4
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| 4, 24, 120, 560, 2520, 11088, 48048, 205920, 875160, 3695120, 15519504, 64899744, 270415600, 1123264800, 4653525600, 19234572480, 79342611480, 326704870800, 1343120024400, 5513861152800, 22606830726480, 92580354403680
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
R. C. Mullin, E. Nemeth and P. J. Schellenberg, The enumeration of almost cubic maps, pp. 281-295 in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computer Science. Vol. 1, edited R. C. Mullin et al., 1970.
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FORMULA
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G.f.: 4*(1-4x)^{-3/2}.
a(n)=1/J(n) where J(n)=integral(t=0,Pi/4,(cos(t)^2-1/2)^(2n+1)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 17 2006
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MAPLE
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seq(sum(n*binomial(2*n, n), k=1..2), n=1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 14 2007
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PROGRAM
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(PARI) a(n)=if(n<0, 0, 4*(2*n+1)!/n!^2)
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CROSSREFS
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a(n)=4 A002457(n).
a(n) = 2 * A005430(n+1) = 4 * A002457(n).
Cf. A001803.
Sequence in context: A037132 A067312 A017976 this_sequence A049315 A098224 A024049
Adjacent sequences: A002008 A002009 A002010 this_sequence A002012 A002013 A002014
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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Simpler description from Travis Kowalski (tkowalski(AT)coloradocollege.edu), Mar 20 2003
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