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Search: id:A135052
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| A135052 |
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Expansion of (1-2x-sqrt(1-4x+8x^3-4x^4))/(2x^2(1-x)). |
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+0
2
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| 1, 1, 3, 7, 19, 51, 143, 407, 1183, 3487, 10415, 31439, 95791, 294191, 909823, 2830943, 8856255, 27839167, 87888767, 278545663, 885903743, 2826612095, 9045147391, 29022168063, 93350430975, 300949170431, 972271227647
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Sequence is the binomial transform of the aerated large Schroeder numbers A006318. Hankel transform is A060656(n+1).
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FORMULA
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a(n)=sum{k=0..n, sum{j=0..k/2, C(k/2+j, 2j)*C(j)*(1+(-1)^k)/2}}, where C(n)=A000108(n).
G.f.: 1/(1-x-2x^2/(1-x-x^2/(1-x-2x^2/(1-x-x^2/(1-x-2x^2.... (continued fraction); [From Paul Barry (pbarry(AT)wit.ie), Jan 02 2009]
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CROSSREFS
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Sequence in context: A002426 A011769 A087432 this_sequence A146597 A115254 A090378
Adjacent sequences: A135049 A135050 A135051 this_sequence A135053 A135054 A135055
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Nov 15 2007
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