OFFSET
1,2
COMMENTS
All terms are powers of 2.
Lim_{n->inf} A285388(n)/a(n) = 2/sqrt(Pi).
LINKS
Indranil Ghosh, Table of n, a(n) for n = 1..40
FORMULA
a(n) is the denominator of Sum_{k=0..n^2-1} (binomial(2k,k)/4^k)/n.
a(n) = denominator of n*binomial(2*n^2, n^2)/2^(2*n^2 -1). - Ralf Steiner, Apr 22 2017
MATHEMATICA
Table[Denominator[Sum[Binomial[2k, k]/4^k, {k, 0, n^2-1}]/n], {n, 1, 10}]
Denominator[Table[2^(1-2 n^2) n Binomial[2 n^2, n^2], {n, 1, 10}]] (* Ralf Steiner, Apr 22 2017 *)
PROG
(Python)
from sympy import binomial, Integer
def a(n): return (Integer(2)**(1-2*n**2) * Integer(n) * binomial(2*n**2, n**2)).denominator() # Indranil Ghosh, Apr 27 2017
(Magma) [Denominator( n*(n^2+1)*Catalan(n^2)/2^(2*n^2-1) ): n in [1..21]]; // G. C. Greubel, Dec 11 2021
(Sage)
def A285389(n): return 2^(2*n^2 - 1 - (n^2).popcount() - valuation(n, 2))
[A285389(n) for n in (1..20)] # G. C. Greubel, Dec 12 2021
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Ralf Steiner, Apr 18 2017
STATUS
approved