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A102319
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A mean binomial transform of the central binomial numbers.
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0
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1, 2, 7, 26, 107, 462, 2065, 9438, 43811, 205622, 972917, 4631838, 22157525, 106406978, 512629551, 2476289106, 11989326771, 58163714118, 282662269717, 1375801775214, 6705710840657, 32724623955882, 159880046446611
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Second binomial transform of A082758 (with interpolated zeros).
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FORMULA
| G.f.: (1/sqrt(1-6x+5x^2)+1/sqrt(1-2x-3x^2))/2; a(n)=sum{k=0..floor(n/2), binomial(n, 2k)binomial(2(n-2k), n-2k)}; a(n)=sum{k=0..n, binomial(n, k)binomial(2k, k)(1+(-1)^(n-k))/2}.
E.g.f.: cosh(x)exp(2x) I_0(2x); - Paul Barry (pbarry(AT)wit.ie), May 01 2005
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CROSSREFS
| Sequence in context: A150567 A000151 A150568 * A006603 A080244 A124542
Adjacent sequences: A102316 A102317 A102318 * A102320 A102321 A102322
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 04 2005
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