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A001689 5th forward differences of factorial numbers A000142.
(Formerly M4531 N1920)
11
44, 309, 2428, 21234, 205056, 2170680, 25022880, 312273360, 4196666880, 60451816320, 929459059200, 15196285843200, 263309095526400, 4820517384883200, 92987329455820800, 1885246675183872000, 40080616912207872000, 891690242177839104000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
A. van Heemert, Cyclic permutations with sequences and related problems, J. Reine Angew. Math., 198 (1957), 56-72.
FORMULA
a(n) = (n^5 + 10*n^4 + 45*n^3 + 100*n^2 + 109*n + 44)*n! - Mitch Harris, Jul 10 2008
E.g.f.: (44 + 45*x + 20*x^2 + 10*x^3 + x^5)/(1 - x)^6. - Ilya Gutkovskiy, Jan 20 2017
a(n) = (n+6)*a(n-1) - (n-1)*a(n-2) with a(0) = 44 and a(1) = 309. Cf. A096307. - Peter Bala, Jul 22 2021
MATHEMATICA
Differences[Table[n!, {n, 0, 25}], 5] (* T. D. Noe, Aug 09 2012 *)
CROSSREFS
Sequence in context: A060836 A135182 A094794 * A306937 A199828 A183633
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)