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%I #7 Sep 08 2022 08:45:41
%S 1,0,0,0,1,0,0,12,12,0,0,216,484,216,0,0,5760,21000,21000,5760,0,0,
%T 216000,1117920,1822500,1117920,216000,0,0,10886400,74088000,
%U 171884160,171884160,74088000,10886400,0,0,711244800,6059370240,18531878400,26391951936,18531878400,6059370240,711244800,0
%N Triangle T(n, k) = (-1)^n * n! * StirlingS1(n, k)*StirlingS1(n, n-k)/binomial(n, k), read by rows.
%H G. C. Greubel, <a href="/A155825/b155825.txt">Rows n = 0..50 of the triangle, flattened</a>
%F T(n, k) = (-1)^n * n! * StirlingS1(n, k)*StirlingS1(n, n-k)/binomial(n, k).
%e Triangle begins as:
%e 1;
%e 0, 0;
%e 0, 1, 0;
%e 0, 12, 12, 0;
%e 0, 216, 484, 216, 0;
%e 0, 5760, 21000, 21000, 5760, 0;
%e 0, 216000, 1117920, 1822500, 1117920, 216000, 0;
%e 0, 10886400, 74088000, 171884160, 171884160, 74088000, 10886400, 0;
%t T[n_, k_]:= (-1)^n*n!*StirlingS1[n, k]StirlingS1[n, n-k]/Binomial[n, k];
%t Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten
%o (Magma) [(-1)^n*Factorial(n)*StirlingFirst(n,k)*StirlingFirst(n,n-k)/Binomial(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jun 03 2021
%o (Sage) flatten([[factorial(n)*stirling_number1(n,k)*stirling_number1(n,n-k)/binomial(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jun 03 2021
%Y Cf. A048994.
%K nonn,tabl
%O 0,8
%A _Roger L. Bagula_, Jan 28 2009
%E Edited by _G. C. Greubel_, Jun 03 2021
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