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Search: id:A099140
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| 1, 6, 56, 576, 6016, 62976, 659456, 6905856, 72318976, 757334016, 7930904576, 83053510656, 869747654656, 9108115685376, 95381425750016, 998847258034176, 10460064284409856, 109539215284371456, 1147109554861899776
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OFFSET
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0,2
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COMMENT
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In general r^n*T(n,(r+2)/r) has g.f. (1-(r+2)x)/(1-2(r+2)x+r^2*x^2), e.g.f. exp((r+2)x)cosh(2sqrt(r+1)x), a(n)=sum{k=0..n, (r+1)^k*binomial(2n,2k)} and a(n)=(1+sqrt(r+1))^(2n)/2+(1-sqrt(r+1))^(2n)/2.
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FORMULA
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G.f.: (1-6x)/(1-12x+16x^2); E.g.f.: exp(6x)cosh(2sqrt(5)x); a(n)=4^n*T(n, 6/4) where T is the Chebyshev polynomial of first kind; a(n)=sum{k=0..n, 5^k*binomial(2n, 2k)}; a(n)=(1+sqrt(5))^(2n)/2+(1-sqrt(5))^(2n)/2.
a(0)=1, a(1)=6, a(n)=12*a(n-1)-16*a(n-2) for n>1 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 08 2009]
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CROSSREFS
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Cf. A081294, A001541, A090965, A083884, A099141, A099142.
Sequence in context: A166177 A093142 A092655 this_sequence A048348 A025749 A053336
Adjacent sequences: A099137 A099138 A099139 this_sequence A099141 A099142 A099143
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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), Sep 30 2004
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