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Search: id:A003046
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| A003046 |
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Product of first n Catalan numbers.
(Formerly M1987)
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+0
8
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| 1, 1, 2, 10, 140, 5880, 776160, 332972640, 476150875200, 2315045555222400, 38883505145515430400, 2285805733484270091494400, 475475022233529990271933132800, 353230394017289429773019124357120000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The volume of a certain polytope (see Chan et al. reference). However, no combinatorial explanation for this is known.
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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).
C. S. Chan et al., On the volume of a certain polytope, Experimental Mathematics, 9 (2000), 91-99.
H. W. Gould, A class of binomial sums and a series transformation, Utilitas Math., 45 (1994), 71-83.
J. W. Moon and M. Sobel, Enumerating a class of nested group testing procedures, J. Combin. Theory, B23 (1977), 184-188.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..60
D. Zeilberger, [math/9811108] Proof of a Conjecture of Chan, Robbins and Yuen
Experimental Mathematics, Home Page
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FORMULA
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C(0)*C(1)*...*C(n), C() = A000108 = Catalan numbers.
a(n) = Sqrt[(2^n)*A069640(n)*/(2*n+1)!/n! ], n>0, where A069640(n) is an inverse determinant of n X n Hilbert-like Matrix with elements M(i,j)=1/(i+j+1). - Alexander Adamchuk (alex(AT)kolmogorov.com), May 17 2006
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MAPLE
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seq(mul(binomial(2*k, k)/(1+k), k=0..n), n=0..13); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 02 2008
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CROSSREFS
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Cf. A003047, A000108, A055746.
Cf. A069640, A005249, A067689.
Sequence in context: A014228 A059475 A156296 this_sequence A137884 A057565 A152804
Adjacent sequences: A003043 A003044 A003045 this_sequence A003047 A003048 A003049
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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