|
| |
|
|
A084261
|
|
A binomial transform of factorial numbers.
|
|
8
| |
|
|
1, 1, 2, 4, 9, 21, 52, 134, 361, 1009, 2926, 8768, 27121, 86373, 282864, 950866, 3277169, 11564353, 41739130, 153919324, 579411641, 2224535125, 8703993420, 34681783422, 140637608089, 580019801201, 2431509498406, 10355296410712
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Binomial transform of A000142 (with interpolated zeros).
Row sums of A161556. Hankel transform is A137704. [From Paul Barry (pbarry(AT)wit.ie), Apr 11 2010]
|
|
|
FORMULA
| a(n)=sum{k=0..floor(n/2), C(n, 2k)k! }; a(n)=sum{k=0..n, C(n, k)(k/2)!(1+(-1)^k)/2 }.
E.g.f.: exp(x)*(1+sqrt(Pi)/2*x*exp(x^2/4)*erf(x/2)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 25 2003
O.g.f.: A(x) = 1/(1-x-x^2/(1-x-x^2/(1-x-2*x^2/(1-x-2*x^2/(1-x-3*x^2/(1-... -x-[(n+1)/2]*x^2/(1- ...))))))) (continued fraction). - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 17 2006
a_n ~ (1/2) * sqrt(Pi*n/e)*(n/2)^(n/2)*exp(-n/2 + sqrt(2n)). - Cecil C Rousseau (ccrousse(AT)memphis.edu), Mar 14 2006: (cf. A002896).
|
|
|
CROSSREFS
| Sequence in context: A000636 A195980 A136753 * A063026 A106219 A198304
Adjacent sequences: A084258 A084259 A084260 * A084262 A084263 A084264
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 26 2003
|
| |
|
|
