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Search: id:A026029
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| A026029 |
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Number of (s(0), s(1), ..., s(2n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,....,n, s(0) = 3, s(2n) = 3. Also T(2n,n), where T is defined in A026022. |
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3
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| 1, 2, 6, 20, 69, 242, 858, 3068, 11050, 40052, 145996, 534888, 1968685, 7276050, 26993490, 100490220, 375287550, 1405622460, 5278838100, 19873977240, 74994427170, 283595947284, 1074568266756, 4079184055640, 15511924233204, 59083160374952, 225384613313944
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Hankel transform is A008619(n+1). [From Paul Barry (pbarry(AT)wit.ie), May 11 2009]
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FORMULA
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Expansion of (1+x^2*C^4)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
a(n)=sum{k=0..n, C(n, k)*sum{i=0..k, C(k, 2i)*A000108(i+1) }}. - Paul Barry (pbarry(AT)wit.ie), Jul 18 2003
a(n)=Sum_{k, 0<=k<=3}A039599(n,k)=A000108(n)+A000245(n)+A000344(n)+A000588(n)=A026012(n)+A000588(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 12 2008]
a(n)=C(2n,n)-C(2n,n-4). [From Paul Barry (pbarry(AT)wit.ie), May 11 2009]
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CROSSREFS
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Sequence in context: A150123 A082679 A094854 this_sequence A078483 A163135 A047036
Adjacent sequences: A026026 A026027 A026028 this_sequence A026030 A026031 A026032
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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