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A185786 Third accumulation array of A107985, by antidiagonals.

%I A185786 #16 Jul 13 2017 11:08:34
%S A185786 1,6,6,21,35,21,56,120,120,56,126,315,405,315,126,252,700,1050,1050,
%T A185786 700,252,462,1386,2310,2695,2310,1386,462,792,2520,4536,5880,5880,
%U A185786 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 A185786 Third accumulation array of A107985, by antidiagonals.
%C A185786 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 A185786   T(n,k)=(n+k+H)C(n+H,H+1)C(k+H,H+1)/(H+2).
%H A185786 G. C. Greubel, <a href="/A185786/b185786.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A185786 T(n,k) = (n+k+3)*C(n+3,4)*C(k+3,4)/5.
%e A185786 Northwest corner:
%e A185786 1....6.....21.....56.....126
%e A185786 6....35....120....315....700
%e A185786 21...120...405....1050...2310
%e A185786 56...315...1050...2695...5880
%t A185786 (See A185784.)
%t A185786 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 A185786 Cf. A185784.
%K A185786 nonn,tabl
%O A185786 1,2
%A A185786 _Clark Kimberling_, Feb 03 2011