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A078817
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Table by antidiagonals giving variants on Catalan sequence: T(n,k)=C(2n,n)*C(2k,k)*(2k+1)/(n+k+1).
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4
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1, 3, 1, 10, 4, 2, 35, 15, 9, 5, 126, 56, 36, 24, 14, 462, 210, 140, 100, 70, 42, 1716, 792, 540, 400, 300, 216, 132, 6435, 3003, 2079, 1575, 1225, 945, 693, 429, 24310, 11440, 8008, 6160, 4900, 3920, 3080, 2288, 1430, 92378, 43758, 30888, 24024, 19404
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Ira Gessel, Super ballot numbers.
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FORMULA
| T(n, k) =A000984(n)*A002457(k)/(n+k+1) =T(k, n)*(2k+1)/(2n+1).
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EXAMPLE
| Rows start: 1,3,10,35,126,462,1716,...; 1,4,15,56,210,792,3003,...; 2,9,36,140,540,2079,8008,...; 5,24,100,400,1575,6160,24024,...; etc.
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CROSSREFS
| Columns include A000108 (catalan), A038629, A078818 and A078819. Rows include A001700, A001791, A007946 and A078820. Diagonals include A002894 and A060150.
Essentially a reflected version of A033820.
Sequence in context: A126954 A176992 A107870 * A091042 A111418 A113187
Adjacent sequences: A078814 A078815 A078816 * A078818 A078819 A078820
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KEYWORD
| nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Dec 07 2002
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