A101926 a(n) = 2^A101925(n).

2, 4, 16, 32, 256, 512, 2048, 4096, 65536, 131072, 524288, 1048576, 8388608, 16777216, 67108864, 134217728, 4294967296, 8589934592, 34359738368, 68719476736, 549755813888, 1099511627776, 4398046511104, 8796093022208

Offset

0,1

Comments

a(n) is the numerator of 2^(2*n+1)*(n!)^2/(2*n+1)/(2*n)!. The corresponding denominator is A001803. - Daniel Suteu, Feb 03 2017

a(n) is the numerator of Integral_{x=-oo..oo} sech(x)^(2*n+2) dx. The corresponding denominator is A001803(n). - Mohammed Yaseen, Jul 25 2023

a(n) is the denominator of (1/Pi) * Integral_{x=0..Pi/2} sin(x)^(2*n) dx. The corresponding numerator is A001790(n). - Mohammed Yaseen, Sep 19 2023

a(n) = numerator(Pi*binomial(n, -1/2)). - Peter Luschny, Dec 05 2024

Links

Table of n, a(n) for n=0..23.

Index to divisibility sequences

Maple

denom((binomial(2n, n)*4^-n)/2); # Stephen Crowley, Mar 05 2007

Mathematica

Table[Numerator[Beta[1, n + 1, 1/2]], {n, 0, 22}] (* Gerry Martens, Nov 13 2016 *)

Crossrefs

Bisection of A036069 and of A086117.

Cf. A001803, A001790, A101925.

Sequence in context: A094384 A053038 A001088 * A087965 A074411 A189838

Adjacent sequences: A101923 A101924 A101925 * A101927 A101928 A101929

Keyword

nonn

Author

Ralf Stephan, Dec 28 2004

Extensions

More terms from Joshua Zucker, May 15 2006

Status

approved