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Search: id:A099141
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| 1, 7, 73, 847, 10033, 119287, 1419193, 16886527, 200931553, 2390878567, 28449011113, 338514191407, 4027973401873, 47928772841047, 570303484727833, 6786029465163487, 80746825394092993, 960804818888214727
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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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LINKS
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Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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G.f.: (1-7x)/(1-14x+25x^2); E.g.f.: exp(7x)cosh(2sqrt(6)x); a(n)=5^n*T(n, 7/5) where T is the Chebyshev polynomial of first kind; a(n)=sum{k=0..n, 6^k*binomial(2n, 2k)}; a(n)=(1+sqrt(6))^(2n)/2+(1-sqrt(6))^(2n)/2.
a(0)=1, a(1)=7, a(n)=14*a(n-1)-25*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, A099140, A099142.
Sequence in context: A121127 A071060 A092444 this_sequence A084768 A106651 A114429
Adjacent sequences: A099138 A099139 A099140 this_sequence A099142 A099143 A099144
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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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