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A004782 2(2n-3)!/n!(n-1)! is an integer. 5
2, 3, 7, 16, 21, 29, 43, 46, 67, 78, 89, 92, 105, 111, 127, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Superset of A081767, as proved by Luke Pebody. Terms not in A081767 include 3,7,127,511,... - Ralf Stephan, Oct 12 2004

See A260642 for A004782 \ A081767. - M. F. Hasler, Nov 11 2015

Equivalently, numbers n such that binomial(2n-3,n-1) = 0 (mod n(n-1)/2), or: binomial(2n-2,n-1) = 0 (mod n^2-n), or: the Catalan number A000108(n-1) is divisible by n-1, i.e., a(k) = A014847(k)+1. Indeed, 2(2n-3)!/n!(n-1)! = 2(2n-2)!/(n!(n-1)!(2n-2)) = C(n-1)/(n-1). - M. F. Hasler, Nov 11 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A014847(n) + 1. - Enrique Pérez Herrero, Feb 03 2013

MATHEMATICA

Select[Range[500], IntegerQ[2 (2 # - 3)!/(#! (# - 1)!)] &] (* Arkadiusz Wesolowski, Sep 06 2011 *)

PROG

(PARI) for(n=2, 999, binomial(2*n-2, n-1)%(n^2-n)||print1(n", "))

(PARI) is_A004782(n)=!binomod(2*n-2, n-1, n^2-n) \\ Using http://home.gwu.edu/~maxal/gpscripts/binomod.gp by M. Alekseyev. - M. F. Hasler, Nov 11 2015

CROSSREFS

Sequence in context: A058698 A058699 A250193 * A049956 A289844 A153056

Adjacent sequences:  A004779 A004780 A004781 * A004783 A004784 A004785

KEYWORD

nonn

AUTHOR

R. K. Guy

EXTENSIONS

Offset corrected and initial term added by Arkadiusz Wesolowski, Sep 06 2011

STATUS

approved

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Last modified August 16 19:44 EDT 2017. Contains 290627 sequences.