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A001689
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5th forward differences of factorial numbers A000142.
(Formerly M4531 N1920)
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11
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44, 309, 2428, 21234, 205056, 2170680, 25022880, 312273360, 4196666880, 60451816320, 929459059200, 15196285843200, 263309095526400, 4820517384883200, 92987329455820800, 1885246675183872000, 40080616912207872000, 891690242177839104000
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OFFSET
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0,1
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REFERENCES
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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).
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LINKS
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FORMULA
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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
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MATHEMATICA
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Differences[Table[n!, {n, 0, 25}], 5] (* T. D. Noe, Aug 09 2012 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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