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A125231
Triangle read by rows: T(n,k) = ceiling((k+1)/2)*binomial(n,k) (0 <= k <= n).
1
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
0,5
COMMENTS
Row sums = A045623: (1, 2, 5, 12, 28, 64, 144, 320, ...).
A125230 is another triangle with row sums = A045623.
EXAMPLE
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;
...
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
MATHEMATICA
Flatten[Table[Ceiling[(k+1)/2]Binomial[n, k], {n, 0, 20}, {k, 0, n}]] (* Harvey P. Dale, Aug 31 2015 *)
CROSSREFS
Sequence in context: A080955 A340108 A340107 * A117919 A309106 A160014
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Nov 24 2006
EXTENSIONS
Edited by N. J. A. Sloane, Dec 02 2006
STATUS
approved