Voozh

A001689

5th forward differences of factorial numbers A000142.

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

T. D. Noe, Table of n, a(n) for n = 0..100

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

A. van Heemert, Cyclic permutations with sequences and related problems, J. Reine Angew. Math., 198 (1957), 56-72.

Index entries for sequences related to factorial numbers

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

Cf. A000142, A001563, A001564, A001565, A001688, A096307.

Sequence in context: A060836 A135182 A094794 * A306937 A199828 A183633

Adjacent sequences: A001686 A001687 A001688 * A001690 A001691 A001692

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

URL: https://oeis.org/A001689

⇱ A001689 - OEIS