A125231 Triangle read by rows: T(n,k) = ceiling((k+1)/2)*binomial(n,k) (0 <= k <= n).
1, 1, 1, 1, 2, 2, 1, 3, 6, 2, 1, 4, 12, 8, 3, 1, 5, 20, 20, 15, 3, 1, 6, 30, 40, 45, 18, 4, 1, 7, 42, 70, 105, 63, 28, 4, 1, 8, 56, 112, 210, 168, 112, 32, 5, 1, 9, 72, 168, 378, 378, 336, 144, 45, 5, 1, 10, 90, 240, 630, 756, 840, 480, 225, 50, 6, 1, 11, 110, 330, 990, 1386, 1848
Offset: 0
Examples
First few rows of the triangle: 1; 1, 1; 1, 2, 2; 1, 3, 6, 2; 1, 4, 12, 8, 3; 1, 5, 20, 20, 15, 3; 1, 6, 30, 40, 45, 18, 4; 1, 7, 42, 70, 105, 63, 28, 4; ...
Programs
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Maple
T:=(n,k)->ceil((k+1)/2)*binomial(n,k): for n from 0 to 12 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form
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Mathematica
Flatten[Table[Ceiling[(k+1)/2]Binomial[n,k],{n,0,20},{k,0,n}]] (* Harvey P. Dale, Aug 31 2015 *)
Extensions
Edited by N. J. A. Sloane, Dec 02 2006
Comments