A125092 Triangle read by rows: T(n,k) = (k+1)^2*binomial(n,k) (0 <= k <= n).

1, 1, 4, 1, 8, 9, 1, 12, 27, 16, 1, 16, 54, 64, 25, 1, 20, 90, 160, 125, 36, 1, 24, 135, 320, 375, 216, 49, 1, 28, 189, 560, 875, 756, 343, 64, 1, 32, 252, 896, 1750, 2016, 1372, 512, 81, 1, 36, 324, 1344, 3150, 4536, 4116, 2304, 729, 100, 1, 40, 405, 1920, 5250, 9072

Offset: 0

Author

Gary W. Adamson, Nov 19 2006

Keywords

• nonn
• tabl

Comments

Binomial transform of the infinite diagonal matrix (1,4,9,16,...).

Sum of entries in row n = (n+1)*(n+4)*2^(n-2) = A001793(n+1).

Examples

			First few rows of the triangle:
  1;
  1,   4;
  1,   8,   9;
  1,  12,  27,  16;
  1,  16,  54,  64,  25;
  1,  20,  90, 160, 125,  36;
  ...
		

Links

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

Crossrefs

Cf. A001793.

Programs

Maple

T:=(n,k)->(k+1)^2*binomial(n,k): for n from 0 to 11 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form

Mathematica

Table[(k+1)^2 Binomial[n,k],{n,0,10},{k,0,n}]//Flatten (* Harvey P. Dale, Feb 20 2023 *)

Extensions

Edited by N. J. A. Sloane, Nov 29 2006