A127943 a(n) = 2^binomial(n+1,2)/A046161(n).

1, 1, 1, 4, 8, 128, 2048, 131072, 2097152, 536870912, 137438953472, 140737488355328, 72057594037927936, 295147905179352825856, 1208925819614629174706176, 19807040628566084398385987584, 40564819207303340847894502572032, 2658455991569831745807614120560689152

Offset: 0

Author

Paul Barry, Feb 08 2007

Keywords

• easy
• nonn

Comments

Apparently, also numerator of 2^(n*(n-1)/2)/n!. - N. J. A. Sloane, Dec 31 2010

Links

• G. C. Greubel, Table of n, a(n) for n = 0..82

Programs

GAP

List([0..30], n-> 2^(Binomial(n+1,2))/DenominatorRat(Binomial(2*n, n)/4^n)); # G. C. Greubel, Dec 09 2018

Magma

[2^(Binomial(n+1,2))/Denominator(Binomial(2*n, n)/4^n): n in [0..25]]; // G. C. Greubel, May 01 2018

Maple

a:=n->2^(binomial(n+1,2))/denom(binomial(2*n,n)/4^n); seq(a(n),n=0..17); # Muniru A Asiru, Dec 10 2018

Mathematica

Table[2^Binomial[n+1,2]/Denominator[Binomial[2*n,n]/4^n], {n, 0, 25}] (* G. C. Greubel, May 01 2018 *)

PARI

for(n=0,25, print1(2^(binomial(n+1,2))/denominator(binomial(2*n, n)/4^n), ", ")) \\ G. C. Greubel, May 01 2018

PARI

a(n) = numerator(2^(n*(n-1)/2)/n!); \\ Altug Alkan, May 02 2018

Sage

[2^binomial(n+1,2)/denominator(binomial(2*n,n)/4^n) for n in range(30)] # G. C. Greubel, Dec 09 2018

Formula

a(n) = 2^binomial(n+1,2)/denominator(binomial(2*n,n)/4^n).

a(n) = 2^A127944(n).