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A258398 Number of 2n-length strings of balanced parentheses of exactly 10 different types that are introduced in ascending order. 2
16796, 3233230, 354660460, 29214542500, 2013190058880, 122762429039250, 6850724997273300, 357603651626578500, 17726205673051976100, 843509478504416874150, 38843740303576863755100, 1741683387026398566250500, 76401095775145069217992560 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,1

COMMENTS

In general, column k>0 of A253180 is asymptotic to (4*k)^n / (k!*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015

LINKS

Alois P. Heinz, Table of n, a(n) for n = 10..600

FORMULA

Recurrence: (n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*n*(n+1)*a(n) = 110*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*n*(2*n - 1)*a(n-1) - 5280*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(2*n - 3)*(2*n - 1)*a(n-2) + 145200*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-3) - 2524368*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-4) + 28865760*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-5) - 218683520*(n-8)*(n-7)*(n-6)*(n-5)*(2*n - 11)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-6) + 1076416000*(n-8)*(n-7)*(n-6)*(2*n - 13)*(2*n - 11)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-7) - 3264915456*(n-8)*(n-7)*(2*n - 15)*(2*n - 13)*(2*n - 11)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-8) + 5441863680*(n-8)*(2*n - 17)*(2*n - 15)*(2*n - 13)*(2*n - 11)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-9) - 3715891200*(2*n - 19)*(2*n - 17)*(2*n - 15)*(2*n - 13)*(2*n - 11)*(2*n - 9)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*a(n-10). - Vaclav Kotesovec, Jun 01 2015

a(n) ~ 40^n / (10!*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015

MAPLE

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

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

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

a:= n-> T(n, 10):

seq(a(n), n=10..25);

CROSSREFS

Column k=10 of A253180.

Sequence in context: A244107 A264183 A258497 * A215550 A227600 A147698

Adjacent sequences:  A258395 A258396 A258397 * A258399 A258400 A258401

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 28 2015

STATUS

approved

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Last modified April 19 21:57 EDT 2021. Contains 343117 sequences. (Running on oeis4.)