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Third accumulation array of A107985, by antidiagonals.
2

%I #16 Jul 13 2017 11:08:34

%S 1,6,6,21,35,21,56,120,120,56,126,315,405,315,126,252,700,1050,1050,

%T 700,252,462,1386,2310,2695,2310,1386,462,792,2520,4536,5880,5880,

%U 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

%N Third accumulation array of A107985, by antidiagonals.

%C 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

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

%H G. C. Greubel, <a href="/A185786/b185786.txt">Table of n, a(n) for the first 50 rows, flattened</a>

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

%e Northwest corner:

%e 1....6.....21.....56.....126

%e 6....35....120....315....700

%e 21...120...405....1050...2310

%e 56...315...1050...2695...5880

%t (See A185784.)

%t 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 *)

%Y Cf. A185784.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Feb 03 2011