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A001688 4th forward differences of factorial numbers A000142.
(Formerly M4636 N1980)
10
9, 53, 362, 2790, 24024, 229080, 2399760, 27422640, 339696000, 4536362880, 64988179200, 994447238400, 16190733081600, 279499828608000, 5100017213491200, 98087346669312000, 1983334021853184000, 42063950934061056000, 933754193111900160000 (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

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

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Index entries for sequences related to factorial numbers

FORMULA

For n>=0 a(n) = n!*(n^4 + 6*n^3 + 17*n^2 + 20*n + 9). - Benoit Cloitre, Jun 10 2004

G.f.: -log(-x+1)+1+2/(x-1)^4*x*(4-3*x+2*x^2). - Simon Plouffe, Master's Thesis, Uqam 1992

E.g.f.: (9 + 8*x + 6*x^2 + x^4)/(1 - x)^5. - Ilya Gutkovskiy, Jan 20 2017

MATHEMATICA

Table[(n^4 + 6*n^3 + 17*n^2 + 20*n + 9) n!, {n, 0, 20}] (* T. D. Noe, Aug 09 2012 *)

Differences[Range[0, 30]!, 4] (* Harvey P. Dale, Jun 06 2017 *)

PROG

(PARI) a(n)=if(n<0, 0, n!*(n^4 + 6*n^3 + 17*n^2 + 20*n + 9))

CROSSREFS

Cf. A000142.

Sequence in context: A295203 A038761 A003698 * A144040 A052108 A209453

Adjacent sequences:  A001685 A001686 A001687 * A001689 A001690 A001691

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 19 04:06 EDT 2019. Contains 323377 sequences. (Running on oeis4.)