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A053991 Number of distinct residues of generalized Catalan number 1/((n^2-1)*k + 1)*binomial(n^2*k, k) modulo n^2 as k runs through the positive integers. 0
3, 4, 6, 5, 17, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Table of n, a(n) for n=2..7.

F. Luca, P. Stanica, Products of factorials modulo p, arXiv:math/0109058 [math.NT], 2001.

P. Stanica, On powerfree p^q-Catalan numbers

P. Stanica, p^q Catalan numbers and squarefree binomial coefficients, arXiv:math/0010148 [math.NT], 2000.

FORMULA

For p prime, p != 5, a(p) = p+1.

{1/((n^2-1)*k+1)*binomial(n^2*k, k) modulo n^2 | k \in N}

EXAMPLE

a(2)=3 since there are 3 residues of 1/((2^2-1)*n + 1)*binomial(2^2*n, n) modulo 2^2, namely {0,1,2}.

CROSSREFS

Sequence in context: A057757 A058838 A001177 * A276814 A198617 A298808

Adjacent sequences:  A053988 A053989 A053990 * A053992 A053993 A053994

KEYWORD

nonn,more

AUTHOR

Pantelimon Stanica (pstanica(AT)mail.aum.edu), Apr 04 2000; corrected Feb 08 2001

STATUS

approved

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Last modified January 23 22:26 EST 2019. Contains 319404 sequences. (Running on oeis4.)