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1, 8, 92, 1184, 15632, 207488, 2757056, 36643328, 487039232, 6473467904, 86042074112, 1143628341248, 15200538791936, 202038000386048, 2685388609667072, 35692849740775424, 474411605904392192
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| G.f.: (1-8x)/(1-16x+36x^2); E.g.f.: exp(8x)cosh(2sqrt(7)x); a(n)=6^n*T(n, 8/6) where T is the Chebyshev polynomial of first kind; a(n)=sum{k=0..n, 7^k*binomial(2n, 2k)}; a(n)=(1+sqrt(7))^(2n)/2+(1-sqrt(7))^(2n)/2.
a(0)=1, a(1)=8, a(n)=16*a(n-1)-36*a(n-2) for n>1 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 08 2009]
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CROSSREFS
| Cf. A081294, A001541, A090965, A083884, A099140, A099141.
Sequence in context: A155615 A133271 A180903 * A007556 A194042 A027395
Adjacent sequences: A099139 A099140 A099141 * A099143 A099144 A099145
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 30 2004
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