A185785 Second accumulation array of A107985, by antidiagonals.

1, 5, 5, 15, 24, 15, 35, 70, 70, 35, 70, 160, 200, 160, 70, 126, 315, 450, 450, 315, 126, 210, 560, 875, 1000, 875, 560, 210, 330, 924, 1540, 1925, 1925, 1540, 924, 330, 495, 1440, 2520, 3360, 3675, 3360, 2520, 1440, 495, 715, 2145, 3900, 5460, 6370, 6370, 5460, 3900, 2145, 715, 1001, 3080, 5775, 8400, 10290, 10976, 10290, 8400, 5775, 3080, 1001

Offset: 1

Author

Clark Kimberling, Feb 03 2011

Keywords

• nonn
• tabl

Comments

See A185784.

Examples

			Northwest corner:
1....5....15....35....70
5....24...70....160...315
15...70...200...450...875
35...160..450...1000..1925
		

Links

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

Crossrefs

Cf. A185784.

Programs

Mathematica

f[n_, k_] := Binomial[k + 2, 3]*Binomial[n + 2, 3]*(n + k + 2)/4;
Table[f[n - k + 1, k], {n, 50}, {k, n, 1, -1}] // Flatten (* G. C. Greubel, Jul 12 2017 *)

Formula

T(n,k) = (n+k+2)*C(n+2,3)*C(k+2,3)/4, k>=1, n>=1.