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A001688
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4th forward differences of factorial numbers A000142.
(Formerly M4636 N1980)
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8
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9, 53, 362, 2790, 24024, 229080, 2399760, 27422640, 339696000, 4536362880, 64988179200, 994447238400, 16190733081600, 279499828608000, 5100017213491200, 98087346669312000, 1983334021853184000, 42063950934061056000, 933754193111900160000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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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).
A. van Heemert, Cyclic permutations with sequences and related problems, J. Reine Angew. Math., 198 (1957), 56-72.
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LINKS
| Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index entries for sequences related to factorial numbers
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FORMULA
| For n>=0 a(n)=n!*(n^4 + 6*n^3 + 17*n^2 + 20*n + 9) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 10 2004
G.f.:-ln(-x+1)+1+2/(x-1)^4*x*(4-3*x+2*x^2), Simon Plouffe, Master's Thesis, Uqam 1992.
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PROG
| (PARI) a(n)=if(n<0, 0, n!*(n^4 + 6*n^3 + 17*n^2 + 20*n + 9))
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CROSSREFS
| Cf. A000142.
Sequence in context: A005025 A038761 A003698 * A144040 A052108 A093846
Adjacent sequences: A001685 A001686 A001687 * A001689 A001690 A001691
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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