A121682 Triangle read by rows: T(i,j) = (T(i-1,j) + i)*i.

1, 6, 4, 27, 21, 9, 124, 100, 52, 16, 645, 525, 285, 105, 25, 3906, 3186, 1746, 666, 186, 36, 27391, 22351, 12271, 4711, 1351, 301, 49, 219192, 178872, 98232, 37752, 10872, 2472, 456, 64, 1972809, 1609929, 884169, 339849, 97929, 22329, 4185, 657, 81, 19728190, 16099390, 8841790, 3398590, 979390, 223390, 41950, 6670, 910, 100

Offset: 1

Author

Thomas Wieder, Aug 15 2006

Keywords

• nonn
• tabl

Comments

The first column is A030297 = a(n) = n*(n+a(n-1)). The main diagonal are the squares A000290 = n^2. The first lower diagonal (6,21,52,...) is A069778 = q-factorial numbers 3!_q. See also A121662.

Examples

			Triangle begins:
      1
      6     4
     27    21     9
    124   100    52   16
    645   525   285  105  25
   3906  3186  1746  666  186  36
  27391 22351 12271 4711 1351 301 49
  ...
		

References

• T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439-445.

Crossrefs

Cf. A030297, A000290, A069778, A121662.

Row sums give A337001.

Programs

Maple

T:= proc(i, j) option remember;
      `if`(j<1 or j>i, 0, (T(i-1, j)+i)*i)
    end:
seq(seq(T(n, k), k=1..n), n=1..10);  # Alois P. Heinz, Jun 22 2022

Mathematica

T[n_, k_] /; 1 <= k <= n := T[n, k] = (T[n-1, k]+n)*n;
T[, ] = 0;
Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 17 2022 *)

Python

def T(i, j): return (T(i-1, j)+i)*i if 1 <= j <= i else 0
print([T(r, c) for r in range(1, 11) for c in range(1, r+1)]) # Michael S. Branicky, Jun 22 2022

Extensions

Edited by N. J. A. Sloane, Sep 15 2006

Formula in name corrected by Alois P. Heinz, Jun 22 2022