OFFSET
3,2
LINKS
G. C. Greubel, Rows n = 3..100 of triangle, flattened
FORMULA
T(n, k) = (n-1)!*n^(n-k)/(2*(n-k)!).
E.g.f.: -(2*log(1+x*LambertW(-y))-2*x*LambertW(-y)+x^2*LambertW(-y)^2)/4.
EXAMPLE
Triangle begins as:
1;
12, 3;
150, 60, 12;
2160, 1080, 360, 60;
36015, 20580, 8820, 2520, 360;
...
MATHEMATICA
f[list_] := Select[list, #>0&]; t = Sum[n^(n-1)x^n/n!, {n, 1, 20}]; Map[f, Drop[Transpose[Table[Range[0, 8]! CoefficientList[Series[t^n/(2n), {x, 0, 8}], x], {n, 3, 8}]], 3]] (* Geoffrey Critzer, Oct 23 2011 *)
Table[k!*Binomial[n, k]*n^(n-k-1)/2, {n, 3, 12}, {k, 3, n}]//Flatten (* G. C. Greubel, May 16 2019 *)
PROG
(PARI) {T(n, k) = k!*binomial(n, k)*n^(n-k-1)/2 }; \\ G. C. Greubel, May 16 2019
(Magma) [[Factorial(k)*Binomial(n, k)*n^(n-k-1)/2: k in [3..n]]: n in [3..12]]; // G. C. Greubel, May 16 2019
(Sage) [[factorial(k)*binomial(n, k)*n^(n-k-1)/2 for k in (3..n)] for n in (3..12)] # G. C. Greubel, May 16 2019
(GAP) Flat(List([3..12], n-> List([3..n], k-> Factorial(k)*Binomial(n, k) *n^(n-k-1)/2 ))); # G. C. Greubel, May 16 2019
CROSSREFS
KEYWORD
AUTHOR
Vladeta Jovovic, Oct 15 2004
STATUS
approved