A171707 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

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, 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