The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A072374 a(1) = 1; a(n) = 1 + Sum_{i=1..n} Product_{j=i..2*i-1} (n-j). 10
1, 2, 3, 6, 11, 24, 51, 122, 291, 756, 1979, 5526, 15627, 46496, 140451, 442194, 1414931, 4687212, 15785451, 54764846, 193129659, 698978136, 2570480147, 9672977706, 36967490691, 144232455524, 571177352091, 2304843053382, 9434493132011, 39289892366736 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A122852 is another version of the same sequence. - R. J. Mathar, Jun 18 2008
LINKS
FORMULA
The sequence 1, 1, 2, 3, .. has a(n)=sum{k=0..floor(n/2), C(n-k, k)k!} (diagonal sums of permutation triangle A008279). - Paul Barry, May 12 2004
Recurrence: 2*a(n) = 3*a(n-1) + (n-1)*a(n-2) - (n-1)*a(n-3). - Vaclav Kotesovec, Feb 08 2014
a(n) ~ sqrt(Pi) * exp(sqrt(n/2) - n/2 + 1/8) * n^((n+1)/2) / 2^(n/2+1) * (1 + 37/(48*sqrt(2*n))). - Vaclav Kotesovec, Feb 08 2014
MATHEMATICA
Table[Sum[Binomial[n-k, k]*k!, {k, 0, Floor[n/2]}], {n, 1, 20}] (* Vaclav Kotesovec, Feb 08 2014 *)
CROSSREFS
Sequence in context: A036648 A047750 A072187 * A122852 A192573 A284994
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 19 2002
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 27 11:41 EDT 2024. Contains 372858 sequences. (Running on oeis4.)