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%I #10 Sep 08 2022 08:45:50
%S 1,1,1,1,0,1,1,-7,-7,1,1,-53,-98,-53,1,1,-383,-966,-966,-383,1,1,
%T -2999,-9384,-12970,-9384,-2999,1,1,-25919,-95880,-166348,-166348,
%U -95880,-25919,1,1,-246959,-1049040,-2177404,-2741806,-2177404,-1049040,-246959,1
%N Triangle read by rows: T(n,k) = 2 - k! + 2*n! - (n-k)! - n!*binomial(n,k).
%C Row sums: {1, 2, 2, -12, -202, -2696, -37734, -576292, -9688610, -179355168, -3644133406, ...}.
%H G. C. Greubel, <a href="/A171707/b171707.txt">Rows n = 0..100 of triangle, flattened</a>
%F T(n,k) = 2 - k! + 2*n! - (n-k)! - n!*binomial(n, k).
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 0, 1;
%e 1, -7, -7, 1;
%e 1, -53, -98, -53, 1;
%e 1, -383, -966, -966, -383, 1;
%e 1, -2999, -9384, -12970, -9384, -2999, 1;
%e ...
%p seq(seq( 2 -k! +2*n! -(n-k)! -n!*binomial(n, k), k=0..n), n=0..10); # _G. C. Greubel_, Nov 28 2019
%t Table[2 -k! +2*n! -(n-k)! -n!*Binomial[n, k], {n,0,10}, {k,0,n}]//Flatten
%o (PARI) T(n,k)= 2 -k! +2*n! -(n-k)! -n!*binomial(n, k); \\ _G. C. Greubel_, Nov 28 2019
%o (Magma) F:=Factorial; [2 -F(k) +2*F(n) -F(n-k) -F(n)*Binomial(n, k): k in [0..n], n in [0..10]]; // _G. C. Greubel_, Nov 28 2019
%o (Sage) f=factorial; [[2 -f(k) +2*f(n) -f(n-k) -f(n)*binomial(n, k) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Nov 28 2019
%o (GAP) F:=Factorial;; Flat(List([0..10], n-> List([0..n], k-> 2 -F(k) +2*F(n) -F(n-k) -F(n)*Binomial(n, k) ))); # _G. C. Greubel_, Nov 28 2019
%K tabl,sign
%O 0,8
%A _Roger L. Bagula_, Dec 15 2009
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