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A123162
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Triangle read by rows: binomial[2*n-1,2*m-1].
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1
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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; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| 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
| 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
| 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
| 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
| Cf. A103327.
Sequence in context: A141523 A201588 A086385 * A083075 A195892 A195522
Adjacent sequences: A123159 A123160 A123161 * A123163 A123164 A123165
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KEYWORD
| nonn,tabl
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 02 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 04 2006
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