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Search: id:A091599
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| A091599 |
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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, 1, 6, 6, 1, 24, 26, 12, 1, 110, 120, 75, 20, 1, 546, 594, 416, 174, 30, 1, 2856, 3094, 2289, 1176, 350, 42, 1, 15504, 16728, 12768, 7322, 2880, 636, 56, 1, 86526, 93024, 72420, 44388, 20475, 6324, 1071, 72, 1, 493350, 528770, 417240, 267240, 136252
(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)(j-1)!(3n-j-k-1)!/[((j-k)!)^2*(2*k-j)!(n-j)! ], j=k..min(n, 2*k))/(2*n-k)!
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EXAMPLE
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1; 2,1; 6,6,1; 24,26,12,1; 110,120,75,20,1;
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MAPLE
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T := proc(n, k) if k<=n then k*sum((2*j-k)*(j-1)!*(3*n-j-k-1)!/(j-k)!/(j-k)!/(2*k-j)!/(n-j)!, j=k..min(n, 2*k))/(2*n-k)! 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 A046646, column 2 gives A046647, row sums give A000259. Same as A046651 but with rows reversed.
Sequence in context: A110098 A130561 A157400 this_sequence A066667 A105278 A008297
Adjacent sequences: A091596 A091597 A091598 this_sequence A091600 A091601 A091602
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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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