OFFSET
1,4
COMMENTS
Row sums are {1, 2, 6, 16, 50, 204, 1078, 6992, 53226, 462340,..} which is A014144(n) - 1 for n>=2.
Row sums are given by (n+1)* !n - !(n+1), for n>=2, where !n is the left factorial (A003422). - G. C. Greubel, Mar 27 2019
LINKS
G. C. Greubel, Rows n=1..100 of triangle, flattened
Fan Chung, R. L. Graham, Primitive juggling sequences, Am. Math. Monthly 115 (3) (2008) 185-194
FORMULA
Given f_b(x) = (1 - Sum_{k=0..n-1} (n-k)*k!*x^k)/(1-(b+1)*x), then
p(x,b) = -f_b(x)*(1-(b+1)*x) = -(1 - Sum_{k=0..n-1} (n-k)*k!*x^k ).
EXAMPLE
Triangle begins with:
1;
1, 1;
2, 2, 2;
3, 3, 4, 6;
4, 4, 6, 12, 24;
5, 5, 8, 18, 48, 120;
6, 6, 10, 24, 72, 240, 720;
7, 7, 12, 30, 96, 360, 1440, 5040;
8, 8, 14, 36, 120, 480, 2160, 10080, 40320;
9, 9, 16, 42, 144, 600, 2880, 15120, 80640, 362880;
MATHEMATICA
p[x_, n_]:= If[n == 1, 1, -(1 - Sum[(n-k)*k!*x^k, {k, 0, n-1}])]; Table[CoefficientList[p[x, n], x], {n, 1, 10}]//Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Mar 12 2008
STATUS
approved