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.

3, 4, 6, 5, 17, 8

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: A349372 A001177 A337878 * 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