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Search: id:A082590
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| A082590 |
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Expansion of 1/((1-2*x)*sqrt(1-4*x)). |
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+0
16
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| 1, 4, 14, 48, 166, 584, 2092, 7616, 28102, 104824, 394404, 1494240, 5692636, 21785872, 83688344, 322494208, 1246068806, 4825743832, 18726622964, 72798509728, 283443548276, 1105144970992, 4314388905704, 16862208539008
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A0344309(n) = (n!/2^n)*a(n). A076729(n) = n!*a(n).
Row sums of A068555 and A112336. - Paul Barry (pbarry(AT)wit.ie), Sep 04 2005
Hankel transform is 2^n*(-1)^C(n+1,2) (A120617). [From Paul Barry (pbarry(AT)wit.ie), Apr 26 2009]
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FORMULA
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a(n) = 2^n*JacobiP(n, 1/2, -1-n, 3).
a(n)=sum{k=0..n+1, binomial(2n+2, k)*sin((n-k+1)*pi/2} - Paul Barry (pbarry(AT)wit.ie), Nov 02 2004
a(n)=sum{k=0..n, 2^(n-k)*binomial(2k, k)}; a(n)=sum{k=0..n, (2k)!(2(n-k))!/(n!k!(n-k)!)}; - Paul Barry (pbarry(AT)wit.ie), Sep 04 2005
a(n)=sum{k=0..n, C(2n,n)C(n,k)/C(2n,2k)} - Paul Barry (pbarry(AT)wit.ie), Mar 18 2007
G.f.: 1/(1-4x+2x^2/(1+x^2/(1-4x+x^2/(1+x^2/(1-4x+x^2/(1+... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Apr 26 2009]
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CROSSREFS
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Sequence in context: A071749 A071753 A071757 this_sequence A085280 A007851 A014325
Adjacent sequences: A082587 A082588 A082589 this_sequence A082591 A082592 A082593
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), May 13 2003
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