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

0,2

Comments

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

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

Example

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), ...

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 *)

Crossrefs

Cf. A004731.

Bisections are A001790 and A101926.

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

Sequence in context: A260319 A146001 A091879 * A338846 A009477 A324658

Adjacent sequences: A036066 A036067 A036068 * A036070 A036071 A036072

Keyword

nonn,easy,nice,frac

Author

N. J. A. Sloane

Status

approved