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Search: id:A036064
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| A036064 |
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Triangle of flag coefficients [ n k ] (numerators of rational parts). |
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+0
2
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| 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 3, 3, 1, 1, 8, 4, 4, 8, 1, 1, 15, 5, 15, 5, 15, 1, 1, 16, 6, 8, 8, 6, 16, 1, 1, 35, 7, 105, 35, 105, 7, 35, 1, 1, 128, 8, 64, 16, 16, 64, 8, 128, 1, 1, 315, 9, 315, 21, 945, 21, 315, 9, 315, 1, 1, 256, 10, 128, 80, 32, 32, 80, 128, 10, 256, 1, 1, 693
(list; table; graph; listen)
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OFFSET
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0,8
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REFERENCES
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D. A. Klain and G.-C. Rota, Introduction to Geometric Probability, Cambridge, p. 69.
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FORMULA
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[ 2m 2k ] = C(2m, 2k)/C(m, k); [ 2m 2k+1 ] = Pi(2m)!/4^m*k!m!(m-k-1)!; [ 2m+1 k ] = 4^kC(m, k)/C(2k, k); [ 2m+1 2k+1 ] = 4^(m-k)C(m, m-k)/C(2m-2k, m-k).
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EXAMPLE
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1; 1 1; 1 Pi/2 1; 1 2 2 1; 1 3Pi/4 3 3Pi/4 1; 1 8/3 4 4 8/3 1; ...
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CROSSREFS
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Cf. A036065.
Sequence in context: A100522 A140408 A047080 this_sequence A090706 A050935 A104769
Adjacent sequences: A036061 A036062 A036063 this_sequence A036065 A036066 A036067
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KEYWORD
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nonn,easy,tabl,nice,frac
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AUTHOR
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njas
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EXTENSIONS
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More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jun 20 2001
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