A144480 T(n,k) = binomial(n, k)*min(k + 1, n - k + 1), triangle read by rows (n >= 0, 0 <= k <= n).
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, 14, 63, 140, 140, 63, 14, 1, 1, 16, 84, 224, 350, 224, 84, 16, 1, 1, 18, 108, 336, 630, 630, 336, 108, 18, 1, 1, 20, 135, 480, 1050, 1512, 1050, 480, 135, 20, 1
Offset: 0
Examples
Triangle begins: 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, 14, 63, 140, 140, 63, 14, 1; 1, 16, 84, 224, 350, 224, 84, 16, 1; 1, 18, 108, 336, 630, 630, 336, 108, 18, 1; 1, 20, 135, 480, 1050, 1512, 1050, 480, 135, 20, 1; ...
Programs
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Mathematica
Table[Table[Binomial[n, m]*If[m <= Floor[n/2], 1 + m, 1 + n - m], {m, 0, n}], {n, 0, 10}] // Flatten -
Maxima
create_list(binomial(n, k)*min(k + 1, n - k + 1), n, 0, 10, k, 0, n); /* Franck Maminirina Ramaharo, Dec 10 2018 */
Formula
Extensions
Entry revised by N. J. A. Sloane, Aug 07 2014
Edited by Franck Maminirina Ramaharo, Dec 10 2018