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A131182 Table T(n,k) = n!*k^n, read by upwards antidiagonals. 3
1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 6, 8, 3, 1, 0, 24, 48, 18, 4, 1, 0, 120, 384, 162, 32, 5, 1, 0, 720, 3840, 1944, 384, 50, 6, 1, 0, 5040, 46080, 29160, 6144, 750, 72, 7, 1, 0, 40320, 645120, 524880, 122880, 15000, 1296, 98, 8, 1, 0, 362880, 10321920, 11022480, 2949120, 375000, 31104, 2058, 128, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

For k>0, T(n,k) is the n-th moment of the exponential distribution with mean = k. - Geoffrey Critzer, Jan 06 2019

LINKS

Table of n, a(n) for n=0..65.

FORMULA

From Ilya Gutkovskiy, Aug 11 2017: (Start)

G.f. of column k: 1/(1 - k*x/(1 - k*x/(1 - 2*k*x/(1 - 2*k*x/(1 - 3*k*x/(1 - 3*k*x/(1 - ...))))))), a continued fraction.

E.g.f. of column k: 1/(1 - k*x). (End)

EXAMPLE

The (inverted) table begins:

k=0: 1, 0,   0,    0,      0,       0, ... (A000007)

k=1: 1, 1,   2,    6,     24,     120, ... (A000142)

k=2: 1, 2,   8,   48,    384,    3840, ... (A000165)

k=3: 1, 3,  18,  162,   1944,   29160, ... (A032031)

k=4: 1, 4,  32,  384,   6144,  122880, ... (A047053)

k=5: 1, 5,  50,  750,  15000,  375000, ... (A052562)

k=6: 1, 6,  72, 1296,  31104,  933120, ... (A047058)

k=7: 1, 7,  98, 2058,  57624, 2016840, ... (A051188)

k=8: 1, 8, 128, 3072,  98304, 3932160, ... (A051189)

k=9: 1, 9, 162, 4374, 157464, 7085880, ... (A051232)

Main diagonal is 1, 1, 8, 162, 6144, 375000, ... (A061711).

MAPLE

T:= (n, k)-> n!*k^n:

seq(seq(T(d-k, k), k=0..d), d=0..12);  # Alois P. Heinz, Jan 06 2019

CROSSREFS

Columns k=0-9 give: A000007, A000142, A000165, A032031, A047053, A052562, A047058, A051188, A051189, A051232.

Main diagonal gives A061711.

Cf. A292783, A303489.

Sequence in context: A130167 A084938 A135898 * A254883 A266599 A093729

Adjacent sequences:  A131179 A131180 A131181 * A131183 A131184 A131185

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Sep 25 2007

STATUS

approved

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Last modified May 27 04:00 EDT 2019. Contains 323597 sequences. (Running on oeis4.)