A185786 Third accumulation array of A107985, by antidiagonals.

1, 6, 6, 21, 35, 21, 56, 120, 120, 56, 126, 315, 405, 315, 126, 252, 700, 1050, 1050, 700, 252, 462, 1386, 2310, 2695, 2310, 1386, 462, 792, 2520, 4536, 5880, 5880, 4536, 2520, 792, 1287, 4290, 8190, 11466, 12740, 11466, 8190, 4290, 1287, 2002, 6930, 13860, 20580, 24696, 24696, 20580, 13860, 6930, 2002, 3003, 10725, 22275, 34650

Offset

1,2

Comments

See A185784. The pattern established by the formulas for A185785, A185786, A185787, suggests that the H-th accumulation array of A107985 may be given by

T(n,k)=(n+k+H)C(n+H,H+1)C(k+H,H+1)/(H+2).

Links

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

Formula

T(n,k) = (n+k+3)*C(n+3,4)*C(k+3,4)/5.

Example

Northwest corner:
1....6.....21.....56.....126
6....35....120....315....700
21...120...405....1050...2310
56...315...1050...2695...5880

Mathematica

(See A185784.)
f[n_, k_] := Binomial[k + 3, 4]*Binomial[n + 3, 4]*(n + k + 3)/5; Table[f[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* G. C. Greubel, Jul 12 2017 *)

Crossrefs

Cf. A185784.

Sequence in context: A198340 A189980 A188273 * A341245 A178822 A253069

Adjacent sequences: A185783 A185784 A185785 * A185787 A185788 A185789

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 03 2011

Status

approved