login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A258399 Number of 4n-length strings of balanced parentheses of exactly n different types that are introduced in ascending order. 4
1, 2, 98, 11880, 2432430, 714249900, 275335499824, 131928199603200, 75727786603836510, 50713478000403718500, 38843740303576863755100, 33508462196084294380001040, 32157574295254903735909896240, 33990046387543889224733323929120 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

FORMULA

a(n) = A253180(2n,n).

a(n) ~ c * d^n * n! / n^(5/2), where d = A256254 = 98.8248737517356857317..., c = 0.04120447463568595292374592925415728563265717672... . - Vaclav Kotesovec, Jun 01 2015

EXAMPLE

a(0) = 1: the empty string.

a(1) = 2: ()(), (()).

a(2) = A000108(4) * (2^3-1) = 14*7 = 98.

MAPLE

ctln:= proc(n) option remember; binomial(2*n, n)/(n+1) end:

A:= proc(n, k) option remember; k^n*ctln(n) end:

a:= n-> add(A(2*n, n-i)*(-1)^i/((n-i)!*i!), i=0..n):

seq(a(n), n=0..15);

CROSSREFS

Cf. A000108, A253180, A256254, A258426.

Sequence in context: A317729 A223038 A324266 * A212838 A024241 A278684

Adjacent sequences:  A258396 A258397 A258398 * A258400 A258401 A258402

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 28 2015

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 December 16 00:33 EST 2019. Contains 330013 sequences. (Running on oeis4.)