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Search: id:A103972
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| A103972 |
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Expansion of (1-sqrt(1-4x-20x^2))/(2x). |
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+0
2
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| 1, 6, 12, 60, 264, 1392, 7392, 41424, 236640, 1384512, 8224896, 49554816, 301884672, 1856878080, 11514915840, 71915838720, 451938731520, 2855705994240, 18132621772800, 115637702461440, 740356410961920
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Image of c(x), the g.f. of the Catalan numbers A000108 under the mapping g(x)->(1+5x)g(x(1+5x)). In general, the image of the Catalan numbers under the mapping g(x)->(1+i*x)g(x(1+i*x)) is given by a(n)=sum{k=0..n, i^(n-k)C(k)C(k+1,n-k)}.
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FORMULA
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G.f. : (1-sqrt(1-4x(1+5x))/(2x); a(n)=sum{k=0..n, 5^(n-k)C(k)C(k+1, n-k)}.
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CROSSREFS
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Sequence in context: A117762 A104362 A123900 this_sequence A121735 A070970 A045780
Adjacent sequences: A103969 A103970 A103971 this_sequence A103973 A103974 A103975
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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), Feb 23 2005
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