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A266241 Integers n such that average of first n Catalan numbers (A000108) is an integer. 0
1, 2, 12, 377, 2504, 342317 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Integers n such that A014137(n-1) is divisible by n.

Corresponding average values are 1, 1, 6875, ...

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

1 is a term because C(0) mod 1 = 1 mod 1 = 0.

2 is a term because (C(0) + C(1)) mod 2 = (1 + 1) mod 2 = 0.

12 is a term because (C(0) + C(1) + ... + C(10) + C(11)) mod 12 = (1 + 1 + ... + 16796 + 58786) mod 12 = 0.

PROG

(PARI) a(n) = sum(k=0, n, (2*k)!/(k!)^2/(k+1)) % (n+1);

for(n=0, 1e5, if(a(n)==0, print1(n+1", ")));

(MAGMA) a:=[1]; catalan:=1; sum:=catalan; for n in [2..350000] do catalan:=(catalan*(4*n-6)) div n; sum+:=catalan; if (sum mod n) eq 0 then a[#a+1]:=n; end if; end for; a; // Jon E. Schoenfield, Dec 25 2015

CROSSREFS

Cf. A000108, A014137.

Sequence in context: A158261 A215956 A251182 * A012547 A009706 A012551

Adjacent sequences:  A266238 A266239 A266240 * A266242 A266243 A266244

KEYWORD

nonn,more

AUTHOR

Altug Alkan, Dec 25 2015

EXTENSIONS

a(6) from Jon E. Schoenfield, Dec 25 2015

STATUS

approved

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Last modified October 18 18:56 EDT 2019. Contains 328197 sequences. (Running on oeis4.)