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Search: id:A133305
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| A133305 |
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(1/n)*Sum[i=0..n-1,C(n,i)*C(n,i-1)*4^i*5^(n-i)], a(0)=1 . |
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4
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OFFSET
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0,2
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COMMENT
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Fifth column of array A103209 .
The Hankel transform of this sequence is 20^C(n+1,2). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 28 2007
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FORMULA
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G.f.: [1-z-(z^2-18z+1]^(1/2)]/(8z). a(n) = Sum_{k, 0<=k<=n}A088617(n,k)*4^k . a(n) = Sum_{k, 0<=k<=n} A060693(n,k)*4^(n-k). a(n) = Sum_{k, 0<=k<=n}C(n+k, 2k)4^k*C(k), C(n) given by A000108 .
a(0)=1, a(n)=a(n-1)+4*Sum_{k, 0<=k<=n-1}a(k)*a(n-1-k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 23 2007
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CROSSREFS
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Cf. A000108 A060693 A103209 A103210 A103211.
Sequence in context: A137233 A001449 A130976 this_sequence A062023 A084095 A121414
Adjacent sequences: A133302 A133303 A133304 this_sequence A133306 A133307 A133308
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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), Oct 18 2007
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