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

2,1

REFERENCES

F. Luca, P. Stanica, "Products of factorials modulo p", manuscript 2001.

LINKS

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

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){{n^2 k} choose {k}} modulo {n^2} | k\in N}

EXAMPLE

a(2)=3 since there are 3 residues of 1/((2^2-1)n+1){{2^2 n} choose {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 October 17 19:36 EDT 2018. Contains 316293 sequences. (Running on oeis4.)