The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A084261 A binomial transform of factorial numbers. 10
 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; text; internal format)
 OFFSET 0,3 COMMENTS Binomial transform of A000142 (with interpolated zeros). Row sums of A161556. Hankel transform is A137704. [Paul Barry, Apr 11 2010] LINKS G. C. Greubel, Table of n, a(n) for n = 0..880 Jonathan Fang, Zachary Hamaker, and Justin Troyka, On pattern avoidance in matchings and involutions, arXiv:2009.00079 [math.CO], 2020. See Proposition 4.13 p. 15. 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, 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, 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). Conjecture: 2*a(n) -4*a(n-1) +(-n+2)*a(n-2) +(n-2)*a(n-3)=0. - R. J. Mathar, Nov 30 2012 MATHEMATICA Table[Sum[Binomial[n, 2*k]*k!, {k, 0, Floor[n/2]}], {n, 0, 50}] (* G. C. Greubel, Jan 24 2017 *) PROG (PARI) for(n=0, 50, print1(sum(k=0, floor(n/2), binomial(n, 2*k)*k!), ", ")) \\ G. C. Greubel, Jan 24 2017 CROSSREFS Sequence in context: A195980 A136753 A289666 * A063026 A106219 A198304 Adjacent sequences:  A084258 A084259 A084260 * A084262 A084263 A084264 KEYWORD easy,nonn AUTHOR Paul Barry, May 26 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 31 08:06 EDT 2021. Contains 346369 sequences. (Running on oeis4.)