The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A325873 T(n, k) = [x^k] Sum_{k=0..n} |Stirling1(n, k)|*FallingFactorial(x, k), triangle read by rows, for n >= 0 and 0 <= k <= n. 2
 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 4, 0, 1, 0, 8, 5, 10, 0, 1, 0, 26, 58, 15, 20, 0, 1, 0, 194, 217, 238, 35, 35, 0, 1, 0, 1142, 2035, 1008, 728, 70, 56, 0, 1, 0, 9736, 13470, 11611, 3444, 1848, 126, 84, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 LINKS EXAMPLE Triangle starts: [0] [1] [1] [0, 1] [2] [0, 0,    1] [3] [0, 1,    0,     1] [4] [0, 1,    4,     0,     1] [5] [0, 8,    5,     10,    0,    1] [6] [0, 26,   58,    15,    20,   0,    1] [7] [0, 194,  217,   238,   35,   35,   0,   1] [8] [0, 1142, 2035,  1008,  728,  70,   56,  0,  1] [9] [0, 9736, 13470, 11611, 3444, 1848, 126, 84, 0, 1] MATHEMATICA p[n_] := Sum[Abs[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(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 Cf. A079642 (variant), A129062, A325872. Sequence in context: A147312 A271423 A019974 * A046781 A244530 A271424 Adjacent sequences:  A325870 A325871 A325872 * A325874 A325875 A325876 KEYWORD nonn,tabl AUTHOR Peter Luschny, Jun 27 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 9 13:39 EDT 2020. Contains 336323 sequences. (Running on oeis4.)