A185730 Array by antidiagonals: T(n,k) = k*(k+1)*n*(n+1)*(k*n-n+2*k+7)/36.

1, 4, 3, 10, 13, 6, 20, 34, 28, 10, 35, 70, 76, 50, 15, 56, 125, 160, 140, 80, 21, 84, 203, 290, 300, 230, 119, 28, 120, 308, 476, 550, 500, 350, 168, 36, 165, 444, 728, 910, 925, 770, 504, 228, 45, 220, 615, 1056, 1400, 1540, 1435, 1120, 696, 300, 55, 286, 825, 1470, 2040, 2380, 2401, 2100, 1560, 930, 385, 66, 364, 1078, 1980, 2850, 3480, 3724, 3528, 2940

Offset

1,2

Comments

This array is a member of a chain of arrays; it is the accumulation array of the array obtain by writing A125764 rectangularly

1...3....6....10...

2...7....15...26...

3...12...27...48...

and it is the weight array of A185731. (Weight and accumulation arrays are defined at A144112.)

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Formula

T(n,k) = k*(k+1)*n*(n+1)*(k*n-n+2*k+7)/36.

Example

Northwest corner:
  1....4....10....20....35
  3....13...34....70....125
  6....28...76....160...290
  10...50...140...300...550
  15...80...230...500...925

Mathematica

f[n_, k_]:=k(1+k)n(1+n)(7+2k-n+k*n)/36;
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]]
Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten

Crossrefs

Cf. A144112, A125764, A185731.

Sequence in context: A081617 A103252 A065763 * A205965 A242391 A241862

Adjacent sequences: A185727 A185728 A185729 * A185731 A185732 A185733

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 01 2011

Status

approved