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Search: id:A091665
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| A091665 |
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Triangle of certain rooted planar maps, read by rows. |
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+0
2
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| 1, 2, 2, 7, 8, 3, 30, 34, 21, 4, 143, 160, 114, 44, 5, 728, 806, 609, 308, 80, 6, 3876, 4256, 3315, 1908, 715, 132, 7, 21318, 23256, 18444, 11420, 5185, 1482, 203, 8, 120175, 130416, 104652, 67856, 34520, 12600, 2814, 296, 9, 690690, 746350, 603801, 404016
(list; table; graph; listen)
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OFFSET
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1,2
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REFERENCES
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W. G. Brown, Enumeration of non-separable planar maps, Canad. J. Math., 15 (1963), 526-545.
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FORMULA
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T(n, k)=ksum((2j-k+1)(j-1)!(3n-k-j)!/[(j-k+1)!(j-k)!(2*k-j-1)!(n-j)! ], j=k..min(n, 2k-1))/(2n-k+1)! for k<=n and T(n, k)=0 for k>n.
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EXAMPLE
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1; 2,2; 7,8,3; 30,34,21,4; 143,160,114,44,5; ...
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MAPLE
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T := proc(n, k) if k<=n then k*sum((2*j-k+1)*(j-1)!*(3*n-k-j)!/(j-k+1)!/(j-k)!/(2*k-j-1)!/(n-j)!, j=k..min(n, 2*k-1))/(2*n-k+1)! else 0 fi end: seq(seq(T(n, k), k=1..n), n=1..11);
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CROSSREFS
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Column 1 gives A006013, column 2 gives A046649, row sums give A000305. Same as A046652 but with rows reversed.
Sequence in context: A021443 A045923 A117779 this_sequence A019905 A019732 A005300
Adjacent sequences: A091662 A091663 A091664 this_sequence A091666 A091667 A091668
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 03 2004
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