A036069 Denominator of rational part of Haar measure on Grassmannian space G(n,1).

1, 2, 1, 4, 3, 16, 5, 32, 35, 256, 63, 512, 231, 2048, 429, 4096, 6435, 65536, 12155, 131072, 46189, 524288, 88179, 1048576, 676039, 8388608, 1300075, 16777216, 5014575, 67108864, 9694845, 134217728, 300540195

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice
• frac

Comments

Also rational part of denominator of Gamma(n/2+1)/Gamma(n/2+1/2) (cf. A004731).

Examples

			1, 1, 1/2*Pi, 2, 3/4*Pi, 8/3, 15/16*Pi, 16/5, 35/32*Pi, 128/35, 315/256*Pi, ...
The sequence Gamma(n/2+1)/Gamma(n/2+1/2), n >= 0, begins 1/Pi^(1/2), (1/2)*Pi^(1/2), 2/Pi^(1/2), (3/4)*Pi^(1/2), (8/3)/Pi^(1/2), (15/16)*Pi^(1/2), (16/5)/Pi^(1/2), ...
		

References

• D. A. Klain and G.-C. Rota, Introduction to Geometric Probability, Cambridge, p. 67.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A004731.

Bisections are A001790 and A101926.

Cf. A004731, A046161, A001790, A001803, A101926.

Programs

Maple

if n mod 2 = 0 then k := n/2; 2*k*Pi*binomial(2*k-1,k)/4^k else k := (n-1)/2; 4^k/binomial(2*k,k); fi;
f:=n->simplify(GAMMA(n/2+1)/GAMMA(n/2+1/2));

Mathematica

Table[ Denominator[ Gamma[n/2+1]/Gamma[n/2+1/2]*Sqrt[Pi]^(1 - 2 Mod[n, 2])], {n, 0, 32}] (* Jean-François Alcover, Jul 16 2012 *)