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%I #15 Jan 06 2019 15:51:45
%S 1,1,1,1,4,1,1,6,6,1,1,8,18,8,1,1,10,30,30,10,1,1,12,45,80,45,12,1,1,
%T 14,63,140,140,63,14,1,1,16,84,224,350,224,84,16,1,1,18,108,336,630,
%U 630,336,108,18,1,1,20,135,480,1050,1512,1050,480,135,20,1
%N T(n,k) = binomial(n, k)*min(k + 1, n - k + 1), triangle read by rows (n >= 0, 0 <= k <= n).
%F If k <= floor(n/2), then T(n,k) = binomial(n, k)*(k + 1), otherwise T(n,k) = binomial(n, k)*(n - k - 1).
%F T(n,k) = A007318(n,k)*A003983(k+1,n-k+1), i.e., term-by term product of Pascal's triangle A007318 and A003983 as a triangle.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 4, 1;
%e 1, 6, 6, 1;
%e 1, 8, 18, 8, 1;
%e 1, 10, 30, 30, 10, 1;
%e 1, 12, 45, 80, 45, 12, 1;
%e 1, 14, 63, 140, 140, 63, 14, 1;
%e 1, 16, 84, 224, 350, 224, 84, 16, 1;
%e 1, 18, 108, 336, 630, 630, 336, 108, 18, 1;
%e 1, 20, 135, 480, 1050, 1512, 1050, 480, 135, 20, 1;
%e ...
%t Table[Table[Binomial[n, m]*If[m <= Floor[n/2], 1 + m, 1 + n - m], {m, 0, n}], {n, 0, 10}] // Flatten
%o (Maxima) create_list(binomial(n, k)*min(k + 1, n - k + 1), n, 0, 10, k, 0, n); /* _Franck Maminirina Ramaharo_, Dec 10 2018 */
%Y Row sums are in A245560.
%Y Cf. A003983, A007318, A168643.
%K nonn,easy,tabl
%O 0,5
%A _Roger L. Bagula_, Oct 11 2008
%E Entry revised by _N. J. A. Sloane_, Aug 07 2014
%E Edited by _Franck Maminirina Ramaharo_, Dec 10 2018
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