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A156006
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A symmetrical triangle based on A009799: a(n,m) = -(m - n)/(m + n)*Binomial[n + m, n]; t(n,m) = If[n == 0, 1, a(n, m) + a(n, n - m)]
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1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 10, 8, 1, 1, 18, 23, 23, 18, 1, 1, 47, 56, 56, 56, 47, 1, 1, 138, 152, 138, 138, 152, 138, 1, 1, 436, 456, 372, 330, 372, 456, 436, 1, 1, 1438, 1465, 1111, 847, 847, 1111, 1465, 1438, 1, 1, 4871, 4906, 3586, 2431, 2002, 2431, 3586
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are:
{1, 2, 4, 10, 28, 84, 264, 858, 2860, 9724, 33592,...}.
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FORMULA
| a(n,m) = -(m - n)/(m + n)*Binomial[n + m, n];
t(n,m) = If[n == 0, 1, a(n, m) + a(n, n - m)]
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EXAMPLE
| {1},
{1, 1},
{1, 2, 1},
{1, 4, 4, 1},
{1, 8, 10, 8, 1},
{1, 18, 23, 23, 18, 1},
{1, 47, 56, 56, 56, 47, 1},
{1, 138, 152, 138, 138, 152, 138, 1},
{1, 436, 456, 372, 330, 372, 456, 436, 1},
{1, 1438, 1465, 1111, 847, 847, 1111, 1465, 1438, 1},
{1, 4871, 4906, 3586, 2431, 2002, 2431, 3586, 4906, 4871, 1}
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MATHEMATICA
| a[n_, m_] = -(m - n)/(m + n)*Binomial[n + m, n];
t[n_, m_] = If[n == 0, 1, a[n, m] + a[n, n - m]];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| A009799
Sequence in context: A056588 A126770 A202979 * A137854 A062715 A100631
Adjacent sequences: A156003 A156004 A156005 * A156007 A156008 A156009
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 01 2009
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