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Search: id:A076025
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| A076025 |
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G.f.: (1-3*x*C)/(1-4*x*C) where C = (1/2-1/2*(1-4*x)^(1/2))/x = g.f. for Catalan numbers A000108. |
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13
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| 1, 1, 5, 26, 137, 726, 3858, 20532, 109361, 582782, 3106550, 16562668, 88314634, 470942044, 2511443268, 13393472616, 71428622337, 380940866574, 2031641406798, 10835261623356, 57787472903502, 308197667445204, 1643712737618748, 8766437439778776, 46754218658948922
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Contribution from Paul Barry (pbarry(AT)wit.ie), Sep 23 2009: (Start)
The Hankel transform of this sequence is 3n+1 or 1,4,7,10,... (A016777).
The Hankel transform of the aeration of this sequence is A016777 doubled, that is, 1,1,4,4,7,7,...
In general, the Hankel transform of [x^n](1-r*xc(x))/(1-(r+1)*xc(x)) is rn+1, and that of the
corresponding aerated sequence is the doubled sequence of rn+1. (End)
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FORMULA
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a(n+1)=sum{k=0..n, 3^k*comb(2n+1, n-k)2(k+1)/(n+k+2)} - Paul Barry (pbarry(AT)wit.ie), Jun 22 2004
a(n+1)=Sum_{k, 0<=k<=n}A039598(n,k)*3^k . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 21 2007
a(n) = Sum_{k, 0<=k<=n}A039599(n,k)*A015518(k), for n>=1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 22 2007
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CROSSREFS
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Cf. A000108, A001700, A049027, A076026.
Sequence in context: A052918 A018903 A083331 this_sequence A161731 A049607 A035029
Adjacent sequences: A076022 A076023 A076024 this_sequence A076026 A076027 A076028
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Oct 29 2002
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