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Second accumulation array of A107985, by antidiagonals.
3

%I #9 Jul 13 2017 22:28:44

%S 1,5,5,15,24,15,35,70,70,35,70,160,200,160,70,126,315,450,450,315,126,

%T 210,560,875,1000,875,560,210,330,924,1540,1925,1925,1540,924,330,495,

%U 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

%N Second accumulation array of A107985, by antidiagonals.

%C See A185784.

%H G. C. Greubel, <a href="/A185785/b185785.txt">Table of n, a(n) for the first 50 rows, flattened</a>

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

%e Northwest corner:

%e 1....5....15....35....70

%e 5....24...70....160...315

%e 15...70...200...450...875

%e 35...160..450...1000..1925

%t f[n_, k_] := Binomial[k + 2, 3]*Binomial[n + 2, 3]*(n + k + 2)/4;

%t Table[f[n - k + 1, k], {n, 50}, {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