A124848 Triangle read by rows: T(n,k) = (k+1)*(k+2)*(k+3)*binomial(n,k)/6 (0 <= k <= n).

1, 1, 4, 1, 8, 10, 1, 12, 30, 20, 1, 16, 60, 80, 35, 1, 20, 100, 200, 175, 56, 1, 24, 150, 400, 525, 336, 84, 1, 28, 210, 700, 1225, 1176, 588, 120, 1, 32, 280, 1120, 2450, 3136, 2352, 960, 165, 1, 36, 360, 1680, 4410, 7056, 7056, 4320, 1485, 220, 1, 40, 450, 2400, 7350

Offset: 0

Author

Gary W. Adamson, Nov 10 2006

Keywords

• nonn
• tabl

Comments

Sum of entries in row n = (2^n/48)*(n+4)*(n^2 + 11n + 12) = A049612(n+1).

Examples

			Triangle starts:
  1;
  1,   4;
  1,   8,  10;
  1,  12,  30,  20;
  1,  16,  60,  80,  35;
  1,  20, 100, 200, 175,  56;
  1,  24, 150, 400, 525, 336,  84;
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000292, A049612.

Programs

Maple

T:=(n,k)->(k+1)*(k+2)*(k+3)*binomial(n,k)/6: for n from 0 to 10 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form

Mathematica

Flatten[Table[(k+1)(k+2)(k+3) Binomial[n,k]/6,{n,0,10},{k,0,n}]] (* Harvey P. Dale, May 14 2012 *)

Extensions

Edited by N. J. A. Sloane, Dec 02 2006