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Search: id:A112019
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| A112019 |
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Sum(C(n,k)*C(n+k,k)^2,k=0..n), where C := binomial. |
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+0
1
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| 1, 5, 55, 749, 11251, 178835, 2949115, 49906925, 860905315, 15071939255, 266982872905, 4774722189275, 86070844191775, 1561948324845095, 28507384046515555, 522867506128197869, 9631571375362268515, 178094411589895650815, 3304192479145474141741, 61487420580006795749999
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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C. Elsner, On recurrence formulae for sums involving binomial coefficients, Fib. Q., 43 (No. 1, 2005), 31-45.
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FORMULA
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a(n) = 3F2( {-n, 1 + n, 1 + n} ; {1, 1} )(-1) [From Olivier GERARD (olivier.gerard(AT)gmail.com), Apr 23 2009]
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MAPLE
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seq(add((multinomial(n+k, n-k, k, k))*binomial(n+k, k), k=0..n), n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 18 2006
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MATHEMATICA
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Table[HypergeometricPFQ[{-n, 1 + n, 1 + n}, {1, 1}, -1], {n, 0, 20}] [From Olivier GERARD (olivier.gerard(AT)gmail.com), Apr 23 2009]
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CROSSREFS
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Sequence in context: A102312 A114909 A038261 this_sequence A131846 A144577 A132865
Adjacent sequences: A112016 A112017 A112018 this_sequence A112020 A112021 A112022
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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), Nov 28 2005
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