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!)
A121680 a(n) = [x^n] (1 + x*(1+x)^(n+1) )^(n+1). 8
1, 2, 12, 76, 655, 6816, 81690, 1109816, 16782399, 278438740, 5016899833, 97368894756, 2021749249403, 44658312247290, 1044437050070340, 25757381769393392, 667470006331599523, 18119105978249333988 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n) is divisible by (n+1): a(n)/(n+1) = A121681(n).
LINKS
FORMULA
a(n) = Sum_{k=0..n+1} C(n+1,k) * C((n+1)*k,n-k).
EXAMPLE
At n=4, a(4) = [x^4] (1 + x*(1+x)^5 )^5 = 655, since
(1 + x*(1+x)^5 )^5 = 1 + 5*x + 35*x^2 + 160*x^3 + 655*x^4 +...
MATHEMATICA
Table[Sum[Binomial[n+1, k] * Binomial[(n+1)*k, n-k], {k, 0, n+1}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 02 2020 *)
PROG
(PARI) a(n)=sum(k=0, n+1, binomial(n+1, k)*binomial((n+1)*k, n-k))
CROSSREFS
Cf. A121681; variants: A121673-A121679.
Sequence in context: A037620 A198474 A285489 * A277478 A081014 A223771
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 15 2006
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 April 16 10:08 EDT 2024. Contains 371698 sequences. (Running on oeis4.)