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%I #11 Nov 19 2017 03:28:52
%S 1,1,1,7,12,6,90,195,180,60,1701,4200,5320,3360,840,42525,114135,
%T 176400,157500,75600,15120,1323652,3764376,6679134,7484400,5155920,
%U 1995840,332640,49329280,146386240,287567280,379387008,332972640,186666480,60540480,8648640
%N Triangle read by rows, T(n, k) = Pochhammer(n, k) * Stirling2(2*n, k + n) for n >= 0 and 0 <= k <= n.
%H G. C. Greubel, <a href="/A293926/b293926.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F T(n, k) = A293617(n, n, k).
%e Triangle starts:
%e [0] 1
%e [1] 1, 1
%e [2] 7, 12, 6
%e [3] 90, 195, 180, 60
%e [4] 1701, 4200, 5320, 3360, 840
%e [5] 42525, 114135, 176400, 157500, 75600, 15120
%e [6] 1323652, 3764376, 6679134, 7484400, 5155920, 1995840, 332640
%p A293926 := (n, k) -> A293617(n, n, k ):
%p seq(seq(A293926(n, k), k=0..n), n=0..7);
%t A293617[m_, n_, k_] := Pochhammer[m, k] StirlingS2[n + m, k + m];
%t A293926Row[n_] := Table[A293617[n, n, k], {k, 0, n}];
%t Table[A293926Row[n], {n, 0, 7}] // Flatten
%o (PARI) for(n=0,10, for(k=0,n, print1(if(n==0 && k==0, 1, ((n+k-1)!/(n-1)!)*stirling(2*n, n + k, 2)), ", "))) \\ _G. C. Greubel_, Nov 19 2017
%Y T(n,0) = Stirling2(2*n,n) = A007820(n), T(n,n) = A000407(n).
%Y Cf. A293617.
%K nonn,tabl
%O 0,4
%A _Peter Luschny_, Oct 22 2017
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