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A067002
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Numerator of sum_{k=0..n} 2^(k-2n) *binomial(2n-2k,n-k)* binomial(n+k,n).
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2
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1, 3, 21, 77, 1155, 4389, 33649, 129789, 4023459, 15646785, 122044923, 477084699, 7474326951, 29322359577, 230389968105, 906200541213, 57090634096419, 225004263791769, 1775033636579511, 7006711723340175, 110706045228774765
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Numerator of e(0,n) (see Maple line).
The generating function of the full fraction is (1-2*x)^(-3/4). - R. J. Mathar, Nov 06 2011
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LINKS
| V. H. Moll. The evaluation of integrals: a personal story, Notices Amer. Math. Soc., 49 (No. 3, March 2002), 311-317.
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FORMULA
| Numerator of 2^n*Gamma(n+3/4)/(Gamma(3/4)*n!). - R. J. Mathar, Nov 06 2011
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EXAMPLE
| 1, 3/2, 21/8, 77/16, 1155/128, 4389/256, 33649/1024, 129789/2048, 4023459/32768 ... = A067002/A046161
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MAPLE
| e := proc(l, m) local k; add(2^(k-2*m)*binomial(2*m-2*k, m-k)*binomial(m+k, m)*binomial(k, l), k=l..m); end;
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CROSSREFS
| Denominators are in A046161.
Sequence in context: A083564 A054646 A109721 * A110450 A102832 A112851
Adjacent sequences: A066999 A067000 A067001 * A067003 A067004 A067005
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KEYWORD
| nonn,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Feb 16 2002
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