OFFSET
1,2
COMMENTS
For the definition of the BG2 matrix coefficients see A161736.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..830
FORMULA
a(n) = numer(sb(n)) with sb(n) = (2^(4*n-5)*(n-1)!^4)/((n-1)*(2*n-2)!^2) and A161736(n) = denom(sb(n)).
a(n) = denominator(Pi*(2*n - 2)*((n - 3/2)!/(n - 1)!)^2). - Peter Luschny, Feb 12 2025
EXAMPLE
sb(1) = 1; sb(2) = 2; sb(3) = 16/9; sb(4) = 128/75; sb(5) = 2048/1225; etc..
MAPLE
nmax := 18; x(1):=0: x(2):=1: for n from 2 to nmax-1 do x(n+1) := A050605(n-2) + x(n) + 3 od: for n from 1 to nmax do a(n) := 2^x(n) od: seq(a(n), n=1..nmax); # End program 1
nmax1 := 20; for n from 0 to nmax1 do y(2*n+1) := A090739(n); y(2*n) := A090739(n) od: z(1) := 0: z(2) := 1: for n from 3 to nmax1 do z(n) := z(n-1) + y(n-1) od: for n from 1 to nmax1 do a(n) := 2^z(n) od: seq(a(n), n=1..nmax1); # End program 2
# Above Maple programs edited by Johannes W. Meijer, Sep 25 2012 and by Peter Luschny, Feb 13 2025
r := n -> Pi*(2*n - 2)*((n - 3/2)!/(n - 1)!)^2: a := n -> denom(simplify(r(n))):
seq(a(n), n = 1..20); # Peter Luschny, Feb 12 2025
MATHEMATICA
sb[1] = 1; sb[2] = 2; sb[n_] := sb[n] = sb[n-1]*4*(n-1)*(n-2)/(2n-3)^2;
Table[sb[n] // Numerator, {n, 2, 20}] (* Jean-François Alcover, Aug 14 2017 *)
PROG
(PARI) vector(20, n, n++; numerator((2^(4*n-5)*(n-1)!^4)/((n-1)*(2*n-2)!^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((2^(4*n-5)*(Factorial(n-1))^4)/((n-1)*(Factorial(2*n-2))^2)): n in [2..20]]; // G. C. Greubel, Sep 26 2018
CROSSREFS
KEYWORD
easy,frac,nonn,changed
AUTHOR
Johannes W. Meijer, Jun 18 2009
EXTENSIONS
Offset set to 1 and a(1) = 1 prepended by Peter Luschny, Feb 13 2025
STATUS
approved