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 A156006 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)] 0
 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; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 4, 10, 28, 84, 264, 858, 2860, 9724, 33592,...}. LINKS 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)] 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} 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[%] CROSSREFS Sequence in context: A126770 A202979 A306326 * A137854 A062715 A100631 Adjacent sequences:  A156003 A156004 A156005 * A156007 A156008 A156009 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 01 2009 STATUS approved

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Last modified June 24 17:58 EDT 2019. Contains 324330 sequences. (Running on oeis4.)