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 A156717 Triangle read by rows: T(n,m) = binomial(n + m - 1, 2*m) + binomial(2*n - m - 2, 2*(n - m - 1)). 1
 2, 2, 2, 2, 6, 2, 2, 11, 11, 2, 2, 17, 30, 17, 2, 2, 24, 63, 63, 24, 2, 2, 32, 115, 168, 115, 32, 2, 2, 41, 192, 375, 375, 192, 41, 2, 2, 51, 301, 748, 990, 748, 301, 51, 2, 2, 62, 450, 1379, 2288, 2288, 1379, 450, 62, 2, 2, 74, 648, 2396, 4823, 6006, 4823, 2396, 648, 74, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Stefano Spezia, First 150 rows of the triangle, flattened. FORMULA T(n,m) = binomial(n + m - 1, 2*m) + binomial(2*n - m - 2, 2*(n - m - 1)). From Stefano Spezia, Dec 26 2018: (Start) T(n,m) = A007318(n + m - 1, 2*m) + A007318(2*n - m - 2, 2*(n - m - 1)). Sum_{m=0..n-1} T(n,m) = A052995(n). (End) EXAMPLE n\m|  0     1     2     3     4     5     6     7     8 ---+--------------------------------------------------- 1  |  2 2  |  2     2 3  |  2     6     2 4  |  2    11    11     2 5  |  2    17    30    17     2 6  |  2    24    63    63    24     2 7  |  2    32   115   168   115    32     2 8  |  2    41   192   375   375   192    41     2 9  |  2    51   301   748   990   748   301    51     2 MAPLE a := (n, m) -> binomial(n+m-1, 2*m)+binomial(2*n-m-2, 2*(n-m-1)): seq(seq(a(n, m), m = 0 .. n-1), n = 1 .. 10) # Stefano Spezia, Dec 26 2018 MATHEMATICA Flatten[Table[Table[Binomial[n + m - 1, 2*m] + Binomial[2*n - m - 2, 2*(n - m - 1)], {m, 0, n - 1}], {n, 1, 10}]] PROG (GAP) Flat(List([1..10], n->List([0..n-1], m->Binomial(n + m - 1, 2*m) + Binomial(2*n - m - 2, 2*(n - m - 1))))); # Stefano Spezia, Dec 26 2018 (PARI) T(n, m) = binomial(n+m-1, 2*m)+binomial(2*n-m-2, 2*(n-m-1)); \\ Stefano Spezia, Dec 26 2018 CROSSREFS Cf. A007318, A052995 (row sums). Sequence in context: A073124 A278260 A070877 * A198889 A329814 A130754 Adjacent sequences:  A156714 A156715 A156716 * A156718 A156719 A156720 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Feb 14 2009 EXTENSIONS Edited by Stefano Spezia, Dec 26 2018 STATUS approved

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Last modified July 28 14:19 EDT 2021. Contains 346335 sequences. (Running on oeis4.)