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A293926 Triangle read by rows, T(n, k) = Pochhammer(n, k) * Stirling2(2*n, k + n) for n >= 0 and 0 <= k <= n.

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