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Search: id:A135573
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| A135573 |
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Array T(n,m) of super ballot numbers read along diagonals. |
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+0
1
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| 1, 3, 1, 10, 2, 2, 35, 5, 3, 5, 126, 14, 6, 6, 14, 462, 42, 14, 10, 14, 42, 1716, 132, 36, 20, 20, 36, 132, 6435, 429, 99, 45, 35, 45, 99, 429, 24310, 1430, 286, 110, 70, 70, 110, 286, 1430, 92378, 4862, 858, 286, 154, 126, 154, 286, 858, 4862, 352716, 16796, 2652, 780
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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First row is A000108. 2nd row is A007054. 3rd row and 4th column are essentially A007272.
1st column is A001700. 2nd column is essentially A000108. 3rd column is A007054.
Main diagonal is A000984.
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LINKS
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Ira M. Gessel, Super ballot numbers, J. Symb. Comput. vol 14, iss 2-3 (1992) pp 179-194.
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FORMULA
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T(n,m)=(2n+1)!(2m)!/[n!m!(m+n+1)! ] .
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EXAMPLE
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Array with rows n>=0 and columns m>=0 starts
...1....1....2....5...14...42..132..429.1430.....
...3....2....3....6...14...36...99..286..858....
..10....5....6...10...20...45..110..286..780....
..35...14...14...20...35...70..154..364..910....
.126...42...36...45...70..126..252..546.1260....
.462..132...99..110..154..252..462..924.1980....
1716..429..286..286..364..546..924.1716.3432....
...
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MAPLE
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T := proc(n, m) (2*n+1)!/n!*(2*m)!/m!/(m+n+1)! ; end: for d from 0 to 12 do for c from 0 to d do printf("%d, ", T(d-c, c)) ; od: od:
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CROSSREFS
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Sequence in context: A008299 A016478 A102430 this_sequence A126953 A134284 A134285
Adjacent sequences: A135570 A135571 A135572 this_sequence A135574 A135575 A135576
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 23 2008
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