OFFSET
2,1
COMMENTS
For the definition of the BG2 matrix coefficients see A161736.
This sequence can be linked with several other sequences, see the Maple programs.
LINKS
G. C. Greubel, Table of n, a(n) for n = 2..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)).
EXAMPLE
sb(2) = 2; sb(3) = 16/9; sb(4) = 128/75; sb(5) = 2048/1225; etc..
MAPLE
nmax := 18; with(Bits): A050605 := proc(a, b) option remember; if(0 = And(a, b)) then RETURN(0); else RETURN(1+A050605(Xor(a, b), 2*And(a, b))); fi; end: for n from 0 to nmax do y(n) := A050605(n, 2) od: x(2):=1: for n from 2 to nmax-1 do x(n+1) := y(n-2) + x(n) + 3 od: for n from 2 to nmax do a(n) := 2^x(n) od: seq(a(n), n=2..nmax);
# End program 1
nmax1 := nmax; A007814 := proc(n) local i, j; if n=0 then RETURN(0); fi; i:=0; j:=n; while j mod 2 <> 1 do i:=i+1; j:=j/2; od: i; end: for n from 0 to nmax1 do A090739(n) := A007814(n) + 3 od: for n from 0 to nmax1 do y(2*n+1) := A090739(n); y(2*n) := A090739(n) od: z(2) := 1: for n from 3 to nmax1 do z(n) := z(n-1) + y(n-1) od: for n from 2 to nmax1 do a(n) := 2^z(n) od: seq(a(n), n=2..nmax1);
# End program 2
# Maple programs edited by Johannes W. Meijer, Sep 25 2012
MATHEMATICA
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
AUTHOR
Johannes W. Meijer, Jun 18 2009
STATUS
approved