|
| |
|
|
A084262
|
|
Binomial transform of double factorials.
|
|
1
| |
|
|
1, 2, 6, 28, 188, 1656, 17992, 232016, 3460368, 58574368, 1109200736, 23230928832, 533139875776, 13304094478208, 358653008619648, 10387075613199616, 321626829363798272, 10602925778746753536, 370770015836513986048
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Binomial transform of A001147.
|
|
|
FORMULA
| a(n) := sum{k=0..n, C(n, k)(2k)!/(k!2^k) }; E.g.f. : exp(x)/(1-2x)^(1/2).
a(n)=(1/sqrt(2*pi))*int(x^n*exp((1-x)/2)/sqrt(x-1),x,1,infty); - Paul Barry (pbarry(AT)wit.ie), Jan 28 2008
G.f.: 1/(1-x-x/(1-2x/(1-x-3x/(1-4x/(1-x-5x/(1-6x/(1-x-7x/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Dec 02 2009]
Let M be the infinite bidiagonal matrix with M(r,r)=1 in the main diagonal, M(r,r+1) = 2r-1, r>=1, odd integers in the superdiagonal, and with the rest zeros. a(n) is the sum of first row terms of M^n. Example: a(4) = 188 = 1 + 4 + 18 + 60 + 105. - Gary W. Adamson, Jun 24 2011
|
|
|
CROSSREFS
| Sequence in context: A100526 A200560 A196555 * A084870 A111342 A008964
Adjacent sequences: A084259 A084260 A084261 * A084263 A084264 A084265
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 26 2003
|
| |
|
|
