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A099237 a(n) = Sum_{k=0..n} binomial(n*(n-k),k). 3
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)

MATHEMATICA

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

CROSSREFS

Sequence in context: A060311 A184947 A207652 * A006220 A020026 A077002

Adjacent sequences:  A099234 A099235 A099236 * A099238 A099239 A099240

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 08 2004

STATUS

approved

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Last modified May 19 03:16 EDT 2019. Contains 323377 sequences. (Running on oeis4.)