A171707 Triangle read by rows: T(n,k) = 2 - k! + 2*n! - (n-k)! - n!*binomial(n,k).

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, 1, -25919, -95880, -166348, -166348, -95880, -25919, 1, 1, -246959, -1049040, -2177404, -2741806, -2177404, -1049040, -246959, 1

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

Sequence in context: A172351 A140136 A281123 * A156722 A152565 A174497

Adjacent sequences: A171704 A171705 A171706 * A171708 A171709 A171710

Keyword

tabl,sign

Author

Roger L. Bagula, Dec 15 2009

Status

approved