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%I #24 Dec 26 2018 05:39:03
%S 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,
%T 32,2,2,41,192,375,375,192,41,2,2,51,301,748,990,748,301,51,2,2,62,
%U 450,1379,2288,2288,1379,450,62,2,2,74,648,2396,4823,6006,4823,2396,648,74,2
%N Triangle read by rows: T(n,m) = binomial(n + m - 1, 2*m) + binomial(2*n - m - 2, 2*(n - m - 1)).
%H Stefano Spezia, <a href="/A156717/b156717.txt">First 150 rows of the triangle, flattened.</a>
%F T(n,m) = binomial(n + m - 1, 2*m) + binomial(2*n - m - 2, 2*(n - m - 1)).
%F From _Stefano Spezia_, Dec 26 2018: (Start)
%F T(n,m) = A007318(n + m - 1, 2*m) + A007318(2*n - m - 2, 2*(n - m - 1)).
%F Sum_{m=0..n-1} T(n,m) = A052995(n).
%F (End)
%e n\m| 0 1 2 3 4 5 6 7 8
%e ---+---------------------------------------------------
%e 1 | 2
%e 2 | 2 2
%e 3 | 2 6 2
%e 4 | 2 11 11 2
%e 5 | 2 17 30 17 2
%e 6 | 2 24 63 63 24 2
%e 7 | 2 32 115 168 115 32 2
%e 8 | 2 41 192 375 375 192 41 2
%e 9 | 2 51 301 748 990 748 301 51 2
%p 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
%t 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}]]
%o (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
%o (PARI) T(n,m) = binomial(n+m-1,2*m)+binomial(2*n-m-2,2*(n-m-1)); \\ _Stefano Spezia_, Dec 26 2018
%Y Cf. A007318, A052995 (row sums).
%K nonn,tabl
%O 1,1
%A _Roger L. Bagula_, Feb 14 2009
%E Edited by _Stefano Spezia_, Dec 26 2018