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A036069 Denominator of rational part of Haar measure on Grassmannian space G(n,1). 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jul 16 2012 *)

CROSSREFS

Cf. A004731.

Bisections are A001790 and A101926.

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

Sequence in context: A260319 A146001 A091879 * A009477 A324658 A105568

Adjacent sequences:  A036066 A036067 A036068 * A036070 A036071 A036072

KEYWORD

nonn,easy,nice,frac

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 7 22:19 EDT 2020. Contains 336279 sequences. (Running on oeis4.)