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A125091
Triangle read by rows: T(n,k) = (1/6)*k*(k+1)*(k+2)*binomial(n,k) (1 <= k <= n).
0
1, 2, 4, 3, 12, 10, 4, 24, 40, 20, 5, 40, 100, 100, 35, 6, 60, 200, 300, 210, 56, 7, 84, 350, 700, 735, 392, 84, 8, 112, 560, 1400, 1960, 1568, 672, 120, 9, 144, 840, 2520, 4410, 4704, 3024, 1080, 165, 10, 180, 1200, 4200, 8820, 11760, 10080, 5400, 1650, 220, 11
OFFSET
1,2
COMMENTS
T(n,n) = n*(n+1)*(n+2)/6 = A000292(n).
Sum_{k=1..n} T(n,k) = 2^n*n*(n+2)*(n+7)/48 = A055585(n-1).
EXAMPLE
Triangle starts:
1;
2, 4;
3, 12, 10;
4, 24, 40, 20;
5, 40, 100, 100, 35;
6, 60, 200, 300, 210, 56;
7, 84, 350, 700, 735, 392, 84;
MAPLE
T:=(n, k)->k*(k+1)*(k+2)*binomial(n, k)/6: for n from 1 to 11 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
MATHEMATICA
Flatten[Table[(k(k+1)(k+2)Binomial[n, k])/6, {n, 20}, {k, n}]] (* Harvey P. Dale, Jan 23 2016 *)
CROSSREFS
Cf. A055585.
Cf. A000292.
Sequence in context: A059662 A259630 A114883 * A209048 A181327 A257503
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Nov 19 2006
EXTENSIONS
Edited by N. J. A. Sloane, Dec 04 2006
STATUS
approved