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A119967
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A transform of the central binomial coefficients C(n,floor(n/2)).
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0
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1, 1, 2, 4, 9, 21, 49, 113, 259, 595, 1376, 3202, 7479, 17499, 40986, 96116, 225755, 531115, 1251310, 2951556, 6968883, 16468775, 38951925, 92204241, 218426037, 517799861, 1228280392, 2915346934, 6923469409, 16450694861, 39107365561
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Inverse binomial transform is A001405 with interpolated zeros.
Hankel transform is 1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,... [From Paul Barry (pbarry(AT)wit.ie), Feb 21 2009]
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FORMULA
| G.f.: 2(1-x)/(1-2x-x^2+sqrt(1-4x+6x^2-4x^3-3x^4)); a(n)=sum{k=0..floor(n/2), C(n,2k)C(k,floor(k/2))}.
G.f.: 1/(1-x-x^2/(1-x-x^2/(1-x+x^2/(1-x+x^2/(1-x-x^2/(1-x-x^2/(1-x+x^2/(1-x+x^2/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Feb 21 2009]
Conjecture: (n+2)*(n-3)*a(n) +(2+2*n-n^2)*a(n-1) +(3*n-5)*(n-2)*a(n-2) -(n-2)*(n-3)*a(n-3) -(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Nov 14 2011
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CROSSREFS
| Sequence in context: A051164 A182904 A101891 * A052921 A018905 A024537
Adjacent sequences: A119964 A119965 A119966 * A119968 A119969 A119970
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KEYWORD
| nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 31 2006
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