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A116853 Difference triangle of factorial numbers read by upward diagonals. 4
1, 1, 2, 3, 4, 6, 11, 14, 18, 24, 53, 64, 78, 96, 120, 309, 362, 426, 504, 600, 720, 2119, 2428, 2790, 3216, 3720, 4320, 5040, 16687, 18806, 21234, 24024, 27240, 30960, 35280, 40320 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This is a subsequence of Euler's difference table A068106 and of A047920 (in a different ordering), since 0! = 1 was left out here. - Georg Fischer, Mar 23 2019

LINKS

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

FORMULA

Take successive difference rows of factorial numbers n! starting with n=1. Reorient into a triangle format.

EXAMPLE

Starting with 1, 2, 6, 24, 120 ... we take the first difference row (A001563), second, third, etc. Reorient into a flush left format, getting:

[1]    1;

[2]    1,   2;

[3]    3,   4,   6;

[4]   11,  14,  18,  24;

[5]   53,  64,  78,  96, 120;

[6]  309, 362, 426, 504, 600, 720;

...

PROG

(Haskell)

a116853 n k = a116853_tabl !! (n-1) !! (k-1)

a116853_row n = a116853_tabl !! (n-1)

a116853_tabl = map reverse $ f (tail a000142_list) [] where

   f (u:us) vs = ws : f us ws where ws = scanl (-) u vs

-- Reinhard Zumkeller, Aug 31 2014

CROSSREFS

Cf. A000142 (factorial numbers).

Cf. A000255 (first column and inverse binomial transform of A000142).

N-th forward differences of A000142: A001563 (1st), A001564 (2nd), A001565 (3rd), A001688 (4th), A001689 (5th).

Cf. A047920 (with 0!, different order), A068106 (with 0!), A180191 (row sums), A246606 (central terms).

Sequence in context: A018297 A050886 A079310 * A066615 A133951 A166081

Adjacent sequences:  A116850 A116851 A116852 * A116854 A116855 A116856

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Feb 24 2006

STATUS

approved

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Last modified October 16 13:51 EDT 2019. Contains 328093 sequences. (Running on oeis4.)