A113052 Binomial(5n,n)/(4n+1) mod 5.

1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,1

Comments

Conjecture: for p prime, mod(C(p*n,n)/((p-1)*n+1),p) is the indicator function of the sequence (p^k-1)/(p-1).

Conjecture is true: see link. - Robert Israel, Jun 11 2018

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Robert Israel, Proof of conjecture

Maple

V:= Vector(1+(5^4-1)/4):
V[[seq(1+(5^k-1)/4, k=0..4)]]:= 1:
convert(V, list); # Robert Israel, Jun 11 2018

Mathematica

Array[Mod[Binomial[5 #, #]/(4 # + 1), 5] &, 105, 0] (* Michael De Vlieger, Jun 11 2018 *)

Crossrefs

Sequence in context: A011642 A016338 A266253 * A369967 A256432 A218171

Adjacent sequences: A113049 A113050 A113051 * A113053 A113054 A113055

Keyword

easy,nonn

Author

Paul Barry, Oct 12 2005

Status

approved