|
Search: id:A099327
|
|
|
| A099327 |
|
Expansion of ((1-x)sqrt(1+2x)+(1+x)sqrt(1-2x))/(2(1-2x)^(5/2)). |
|
+0
3
|
|
| 1, 5, 16, 45, 117, 291, 700, 1646, 3799, 8647, 19448, 43330, 95738, 210094, 458216, 994204, 2146955, 4617439, 9893376, 21128058, 44982486, 95510090, 202278376, 427425860, 901236582, 1896594966, 3983929680, 8354539156, 17492095604
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
The g.f. is transformed to 1/(1-x)^5 under the Chebyshev transformation A(x)->1/(1+x^2)A(x/(1+x^2)). Second binomial transform of the sequence with g.f. 1/c(-x)^3, where c(x) is the g.f. of the Catalan numbers A000108.
|
|
FORMULA
|
a(n)=sum{k=0..n, (k+1)binomial(n, (n-k)/2)binomial(k+4, 4)(1+(-1)^(n-k))/(n+k+2)}.
|
|
CROSSREFS
|
Cf. A099325, A099326.
Adjacent sequences: A099324 A099325 A099326 this_sequence A099328 A099329 A099330
Sequence in context: A079094 A053220 A048777 this_sequence A004146 A071101 A110580
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Oct 12 2004
|
|
|
Search completed in 0.002 seconds
|
