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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099237 a(n) = Sum_{k=0..n} binomial(n*(n-k), k). 4
1, 1, 3, 10, 45, 251, 1624, 11908, 97545, 880660, 8664546, 92096731, 1050304775, 12778138842, 165033693175, 2253204163256, 32401745953105, 489207829112931, 7733130368443057, 127664099576228184, 2196149923000824756 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Main diagonal of A099233.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..490

FORMULA

From Vaclav Kotesovec, Feb 19 2018: (Start)

a(n)^(1/n) ~ n^(n/w) * (n+1-w)^(1 - (n+1)/w) * (w-1)^(1/w - 1), where w = LambertW(exp(1)*n),

a(n)^(1/n) ~ n/log(n), but the convergence is too slow.

(End)

MAPLE

A099237:= n-> add( binomial(n*j, n-j), j=0..n );

seq(A099237(n), n=0..30); # G. C. Greubel, Mar 09 2021

MATHEMATICA

Table[Sum[Binomial[n*(n - k), k], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Feb 19 2018 *)

PROG

(Sage)

def A099237(n): return sum( binomial(n*j, n-j) for j in (0..n))

[A099237(n) for n in (0..30)] # G. C. Greubel, Mar 09 2021

(Magma)

A099237:= func< n | (&+[Binomial(n*j, n-j): j in [0..n]]) >;

[A099237(n): n in [0..30]]; // G. C. Greubel, Mar 09 2021

CROSSREFS

Cf. A099233, A157114.

Sequence in context: A184947 A330250 A207652 * A006220 A020026 A077002

Adjacent sequences:  A099234 A099235 A099236 * A099238 A099239 A099240

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 08 2004

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 21 10:09 EDT 2021. Contains 345360 sequences. (Running on oeis4.)