OFFSET
1,3
COMMENTS
Row sums are: {1, 1, 4, -4, 276, -6348, 254976, -13188096, 887086080, ...}.
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
FORMULA
T(n, k) = n! * StirlingS1(n, k)/ binomial(n, k).
EXAMPLE
The triangle begins as:
1;
-1, 2;
4, -6, 6;
-36, 44, -36, 24;
576, -600, 420, -240, 120;
-14400, 13152, -8100, 4080, -1800, 720;
518400, -423360, 233856, -105840, 42000, -15120, 5040;
-25401600, 18817920, -9455040, 3898944, -1411200, 463680, -141120, 40320;
MAPLE
A142473:= (n, k)-> n!*Stirling1(n, k)/binomial(n, k);
seq(seq(A142473(n, k), k=1..n), n=1..12); # G. C. Greubel, Apr 02 2021
MATHEMATICA
T[n_, k_]:= n!*StirlingS1[n, k]/Binomial[n, k];
Table[T[n, k], {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 02 2021 *)
PROG
(Magma)
A142473:= func< n, k | Factorial(n)*StirlingFirst(n, k)/Binomial(n, k) >;
[A142473(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 02 2021
(Sage)
def A142473(n, k): return (-1)^(n-k)*factorial(n)*stirling_number1(n, k)/binomial(n, k)
flatten([[A142473(n, k) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Apr 02 2021
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Roger L. Bagula and Gary W. Adamson, Sep 21 2008
EXTENSIONS
Edited by G. C. Greubel, Apr 02 2021
STATUS
approved