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

1,2

Comments

See A185784.

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A185784.

Sequence in context: A188272 A104551 A100746 * A185905 A341244 A050341

Adjacent sequences: A185782 A185783 A185784 * A185786 A185787 A185788

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 03 2011

Status

approved