|
Search: id:A099142
|
|
| |
|
| 1, 8, 92, 1184, 15632, 207488, 2757056, 36643328, 487039232, 6473467904, 86042074112, 1143628341248, 15200538791936, 202038000386048, 2685388609667072, 35692849740775424, 474411605904392192
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
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.
|
|
LINKS
|
Index entries for sequences related to Chebyshev polynomials.
|
|
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]
|
|
CROSSREFS
|
Cf. A081294, A001541, A090965, A083884, A099140, A099141.
Sequence in context: A116149 A155615 A133271 this_sequence A007556 A027395 A113353
Adjacent sequences: A099139 A099140 A099141 this_sequence A099143 A099144 A099145
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Sep 30 2004
|
|
|
Search completed in 0.002 seconds
|
