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Search: id:A036069
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| A036069 |
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Denominator of rational part of Haar measure on Grassmannian space G(n,1). |
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+0
4
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| 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
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OFFSET
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0,2
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COMMENT
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Also rational part of denominator of GAMMA(n/2+1)/GAMMA(n/2+1/2) (cf. A004731).
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REFERENCES
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D. A. Klain and G.-C. Rota, Introduction to Geometric Probability, Cambridge, p. 67.
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EXAMPLE
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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), ...
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MAPLE
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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));
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CROSSREFS
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Cf. A004731.
Bisections are A001790 and A101926.
Cf. A004731, A046161, A001790, A001803, A101926.
Sequence in context: A099331 A146001 A091879 this_sequence A009477 A105568 A004175
Adjacent sequences: A036066 A036067 A036068 this_sequence A036070 A036071 A036072
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KEYWORD
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nonn,easy,nice,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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