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Search: id:A126087
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| A126087 |
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Expansion of c(2x^2)/(1-xc(2x^2)), where c(x) = (1-sqrt(1-4x))/(2x) is the g.f. of the Catalan numbers (A000108). |
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+0
6
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| 1, 1, 3, 5, 15, 29, 87, 181, 543, 1181, 3543, 7941, 23823, 54573, 163719, 381333, 1143999, 2699837, 8099511, 19319845, 57959535, 139480397, 418441191, 1014536117, 3043608351, 7426790749, 22280372247, 54669443141, 164008329423
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Series reversion of x(1+x)/(1+2x+3x^2) [offset 0]. - Paul Barry (pbarry(AT)wit.ie), Mar 13 2007
Hankel transform is 2^C(n+1,2). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 16 2007
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FORMULA
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G.f.=[1-sqrt(1-8x^2)]/[x(4x-1+sqrt(1-8x^2))]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 04 2007
a(n)=Sum_{k, 0<=k<=n}2^(n-k)*A120730(n,k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 16 2008]
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MAPLE
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c:=x->(1-sqrt(1-4*x))/2/x: G:=c(2*x^2)/(1-x*c(2*x^2)): Gser:=series(G, x=0, 35): seq(coeff(Gser, x, n), n=0..32); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 04 2007
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CROSSREFS
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Cf. A000108.
Sequence in context: A166956 A048738 A018454 this_sequence A148498 A127978 A018470
Adjacent sequences: A126084 A126085 A126086 this_sequence A126088 A126089 A126090
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KEYWORD
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nonn
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 03 2007
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 04 2007
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