OFFSET
0,8
COMMENTS
Row sums: {1, 2, 2, -12, -202, -2696, -37734, -576292, -9688610, -179355168, -3644133406, ...}.
LINKS
G. C. Greubel, Rows n = 0..100 of triangle, flattened
FORMULA
T(n,k) = 2 - k! + 2*n! - (n-k)! - n!*binomial(n, k).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 0, 1;
1, -7, -7, 1;
1, -53, -98, -53, 1;
1, -383, -966, -966, -383, 1;
1, -2999, -9384, -12970, -9384, -2999, 1;
...
MAPLE
seq(seq( 2 -k! +2*n! -(n-k)! -n!*binomial(n, k), k=0..n), n=0..10); # G. C. Greubel, Nov 28 2019
MATHEMATICA
Table[2 -k! +2*n! -(n-k)! -n!*Binomial[n, k], {n, 0, 10}, {k, 0, n}]//Flatten
PROG
(PARI) T(n, k)= 2 -k! +2*n! -(n-k)! -n!*binomial(n, k); \\ G. C. Greubel, Nov 28 2019
(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
(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
(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
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Roger L. Bagula, Dec 15 2009
STATUS
approved