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Search: id:A123162
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| A123162 |
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Triangle read by rows: binomial[2*n-1,2*m-1]. |
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+0
2
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| 1, 1, 1, 1, 3, 1, 1, 5, 10, 1, 1, 7, 35, 21, 1, 1, 9, 84, 126, 36, 1, 1, 11, 165, 462, 330, 55, 1, 1, 13, 286, 1287, 1716, 715, 78, 1, 1, 15, 455, 3003, 6435, 5005, 1365, 105, 1, 1, 17, 680, 6188, 19448, 24310, 12376, 2380, 136, 1, 1, 19, 969, 11628, 50388, 92378, 75582
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Column k has g.f. x^k*sum{j=0..k, C(2k,2j)*x^j}/(1-x)^(2k+0^k); - Paul Barry (pbarry(AT)wit.ie), May 26 2008
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FORMULA
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a(n,m) = If [n == m == 0 || m == 0, 1, (2*n - 1)!/((2*(n - m))!*(2*m - 1)!)]
a(n,k)=C(2n-1,2k-1)+0^n+0^k+0^(n+k); - Paul Barry (pbarry(AT)wit.ie), May 26 2008
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EXAMPLE
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1
1, 1
1, 3, 1
1, 5, 10, 1
1, 7, 35, 21, 1
1, 9, 84, 126, 36, 1
1, 11, 165, 462, 330, 55, 1
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MATHEMATICA
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t[n_, m_] = If [n == m == 0 || m == 0, 1, (2*n - 1)!/((2*(n - m))!*(2*m - 1)!)]; a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Sequence in context: A118538 A141523 A086385 this_sequence A083075 A069972 A115017
Adjacent sequences: A123159 A123160 A123161 this_sequence A123163 A123164 A123165
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 02 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 04 2006
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