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Search: id:A006588
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| A006588 |
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4^n*(3*n)!/((2*n)!*n!). |
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+0
2
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| 1, 12, 240, 5376, 126720, 3075072, 76038144, 1905131520, 48199827456, 1228623052800, 31504481648640, 811751838842880, 20999667135283200, 545086744471535616, 14189559697354260480, 370298578584748425216
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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W. A. Whitworth, DCC Exercises in Choice and Chance, Stechert, NY, 1945, p. 35.
The right-hand side of a binomial coefficient identity in H. W. Gould, Combinatorial Identities, Morgantown, 1972; Eq. 3.115, page 35.
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FORMULA
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Sum_{k=0..n} binomial(4n+1, 2n-2k)*binomial(n+k, k) = 4^n*binomial(3n, n).
a(n) ~ 1/2*3^(1/2)*pi^(-1/2)*n^(-1/2)*3^(3*n)*{1 - 7/72*n^-1 + ...} - Joe Keane (jgk(AT)jgk.org), Jun 11 2002
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MAPLE
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A006588 := n->add( binomial(4*n+1, 2*n-2*k)*binomial(n+k, k), k=0..n);
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MATHEMATICA
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Table[4^n*(3*n)!/((2*n)!*n!), {n, 0, 20}] - Erich Friedman (efriedma(AT)stetson.edu), Mar 22 2008
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PROGRAM
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(PARI) f(n) = 4^n*(3*n)!/((2*n)!*n!) or g(n) = sum(k=0, n, binomial(4*n+1, 2*n-2*k)*binomial(n+k, k)) - P L Patodia (pannalal(AT)usa.net), Feb 24 2007
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CROSSREFS
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Sequence in context: A012303 A119837 A012538 this_sequence A009150 A009080 A002166
Adjacent sequences: A006585 A006586 A006587 this_sequence A006589 A006590 A006591
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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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