|
| |
|
|
A110491
|
|
Expansion of sqrt(1+2x)/sqrt(1-2x).
|
|
0
| |
|
|
1, 2, 4, 24, 144, 1440, 14400, 201600, 2822400, 50803200, 914457600, 20118067200, 442597478400, 11507534438400, 299195895398400, 8975876861952000, 269276305858560000, 9155394399191040000, 311283409572495360000
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Row sums of exponential Riordan array [1, arctanh(2x)]. - Paul Barry (pbarry(AT)wit.ie), Apr 17 2008
|
|
|
FORMULA
| E.g.f. : sqrt((1+2x)/(1-2x)); a(n)=2*n!*binomial(n-1, floor((n-1)/2))+0^n.
The sequence 0,1,0,2,0,4,... has e.g.f. arctanh(x). - Paul Barry (pbarry(AT)wit.ie), Apr 17 2008
|
|
|
MATHEMATICA
| With[{nn=20}, CoefficientList[Series[Sqrt[1+2x]/Sqrt[1-2x], {x, 0, nn}], x] Range[0, nn]!] (* or *) Join[{1}, Table[2n!Binomial[n-1, Floor[(n-1)/2]], {n, 20}]](* From Harvey P. Dale, Nov 11 2011 *)
|
|
|
CROSSREFS
| Cf. A000246, A002867.
Sequence in context: A164313 A087981 A002875 * A019010 A009672 A018988
Adjacent sequences: A110488 A110489 A110490 * A110492 A110493 A110494
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 22 2005
|
| |
|
|
