Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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