OFFSET
0,5
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows 0 <= n <= 150, flattened).
Gabriella Bretti, Pierpaolo Natalini and Paolo E. Ricci, A new set of Sheffer-Bell polynomials and logarithmic numbers, Georgian Mathematical Journal, Feb. 2019, page 8.
Marin Knežević, Vedran Krčadinac, and Lucija Relić, Matrix products of binomial coefficients and unsigned Stirling numbers, arXiv:2012.15307 [math.CO], 2020.
EXAMPLE
Triangle starts:
[0] [1]
[1] [0, 1]
[2] [0, -2, 1]
[3] [0, 7, -6, 1]
[4] [0, -35, 40, -12, 1]
[5] [0, 228, -315, 130, -20, 1]
[6] [0, -1834, 2908, -1485, 320, -30, 1]
[7] [0, 17582, -30989, 18508, -5005, 665, -42, 1]
[8] [0, -195866, 375611, -253400, 81088, -13650, 1232, -56, 1]
[9] [0, 2487832, -5112570, 3805723, -1389612, 279048, -32130, 2100, -72, 1]
MATHEMATICA
p[n_] := Sum[StirlingS1[n, k] FactorialPower[x, k] , {k, 0, n}];
Table[CoefficientList[FunctionExpand[p[n]], x], {n, 0, 9}] // Flatten
PROG
(Sage)
def a_row(n):
s = sum((-1)^(n-k)*stirling_number1(n, k)*falling_factorial(x, k) for k in (0..n))
return expand(s).list()
[a_row(n) for n in (0..9)]
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Peter Luschny, Jun 27 2019
STATUS
approved