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A081767 Numbers n such that n^2-1 divides binomial(2n,n). 6
2, 16, 21, 29, 43, 46, 67, 78, 89, 92, 105, 111, 141, 154, 157, 171, 188, 191, 205, 210, 211, 221, 229, 232, 239, 241, 267, 277, 300, 309, 313, 316, 323, 326, 331, 346, 369, 379, 415, 421, 430, 436, 441, 443, 451, 460, 461, 465, 469, 477, 484, 494, 497, 528 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Is a(n) asymptotic to c*n with 9 < c < 10 ?

A subset of A004782: 2(2n-3)!/n!(n-1)! is an integer.

Equivalently, numbers n such that n-1 divides A000108(n), the n-th Catalan number. - M. F. Hasler, Nov 11 2015

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

Subsequence of A094575.

Sequence in context: A323193 A050850 A082475 * A093026 A271627 A118954

Adjacent sequences:  A081764 A081765 A081766 * A081768 A081769 A081770

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Apr 09 2003

STATUS

approved

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Last modified November 22 00:32 EST 2019. Contains 329383 sequences. (Running on oeis4.)