OFFSET
1,1
COMMENTS
Is a(n) asymptotic to c*n with 9 < c < 10?
A subset of A004782: numbers k such that 2(2k-3)!/(k!(k-1)!) is an integer.
Equivalently, numbers k such that k-1 divides A000108(k), the k-th Catalan number. - M. F. Hasler, Nov 11 2015
The data does not appear to support the conjectured asymptote statement (neither the constant nor being linear). - Bill McEachen, Feb 26 2024
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems, sect. III: Binomial coefficients modulo integers, binomod.gp (v.1.4, 11/2015).
MATHEMATICA
Select[Range[2, 600], Divisible[Binomial[2#, #], #^2-1]&] (* Harvey P. Dale, May 11 2013 *)
PROG
(PARI) for(n=2, 999, binomial(2*n, n)%(n^2-1)||print1(n", ")) \\ M. F. Hasler, Nov 11 2015
(PARI) is_A081767(n)=!binomod(2*n, n, n^2-1) \\ Using binomod.gp by Max Alekseyev, cf. links. - M. F. Hasler, Nov 11 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Apr 09 2003
STATUS
approved