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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

Table of n, a(n) for n=0..54.

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

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