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A160823
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A transform of the large Schroeder numbers.
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0
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1, 1, 3, 5, 13, 27, 69, 161, 415, 1033, 2701, 6983, 18521, 49041, 131723, 354493, 962381, 2620675, 7178285, 19724513, 54430023, 150641937, 418294813, 1164528399, 3250685297, 9094701729, 25501672595, 71649158709, 201687341901
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Hankel transform is A060656(n+1).
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FORMULA
| G.f.: 1/(1-x-2x^2/(1-x^2/(1-x-2x^2/(1-x^2/(1-x-2x^2/(1-x^2/(1-... (continued fraction);
G.f.: (1-x-x^2-sqrt(1-2x-5x^2+6x^3+x^4))/(2x^2(1-x)).
a(n)=sum{k=0..floor(n/2), C(n-k,k)*A006318(k)}.
Conjecture: (n+2)*a(n) -3*(n+1)*a(n-1) +3(2-n)*a(n-2) +(11*n-20)*a(n-3) +(11-5*n)*a(n-4) + (4-n)*a(n-5)=0. - R. J. Mathar, Nov 16 2011
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CROSSREFS
| Sequence in context: A026569 A035082 A005198 * A077443 A147196 A110225
Adjacent sequences: A160820 A160821 A160822 * A160824 A160825 A160826
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 27 2009
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