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Search: id:A106261
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| A106261 |
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Expansion of 1/sqrt(1-20x-20x^2). |
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+0
5
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| 1, 10, 160, 2800, 51400, 970000, 18640000, 362800000, 7128700000, 141103000000, 2809273600000, 56197096000000, 1128614356000000, 22741607080000000, 459548117440000000, 9309106936000000000, 188980474087000000000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Central coefficient of (1+10x+30x^2)^n. Tenth binomial transform of 1/sqrt(1-120x^2). In general, 1/sqrt(1-4*r*x-4*r*x^2) has e.g.f. exp(2rx)BesselI(0,2r*sqrt((r+1)/r)x)), a(n)=sum{k=0..n, C(2k,k)C(k,n-k)r^k}, gives the central coefficient of (1+(2r)x+r(r+1)x^2), and is the (2r)-th binomial transform of 1/sqrt(1-8*C(n+1,2)x^2).
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FORMULA
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E.g.f.: exp(10*x)*BesselI(0, 10*sqrt(6/5)*x); a(n)=sum{k=0..n, C(2k, k)C(k, n-k)5^k}.
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CROSSREFS
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Cf. A006139, A106258, A106259, A106260.
Adjacent sequences: A106258 A106259 A106260 this_sequence A106262 A106263 A106264
Sequence in context: A129460 A087961 A116041 this_sequence A112125 A090374 A034724
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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), Apr 28 2005
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