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A002776
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Terms in certain determinants.
(Formerly M3972 N1642)
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2
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1, 5, 34, 258, 2136, 19320, 190800, 2051280, 23909760, 300827520, 4067884800, 58877280000, 908666035200, 14901260774400, 258832346572800, 4748165630208000, 91746433658880000, 1862735060938752000, 39649900359573504000, 883021783867711488000
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OFFSET
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0,2
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COMMENTS
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a(n) equals (n+1)^2 times the permanent of the (n+1) X (n+1) matrix with 1/(n+1) in the top right corner, 1/(n+1) in the bottom left corner, and 1's everywhere else. - John M. Campbell, May 25 2011
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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^3 + n^2 + 2*n + 1)*n!.
a(n) = (n+3)! - 5*(n+2)! + 6*(n+1)! - n!. - Umut Özer, Dec 26 2017
E.g.f.: (1 + x + 3*x^2 + x^3)/(1 - x)^4. - Stefano Spezia, Apr 17 2022
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MAPLE
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A002776 := [seq(factorial(n+3) - 5 * factorial(n+2) + 6 * factorial(n+1) - factorial(n), n=0..100)]; # Muniru A Asiru, Jan 15 2018
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MATHEMATICA
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PROG
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(GAP) A002776 := List([0..100], n -> Factorial(n+3) - 5 * Factorial(n+2) + 6 * Factorial(n+1) - Factorial(n)); # Muniru A Asiru, Jan 15 2018
(Magma) [(n^3+n^2+2*n+1)*Factorial(n): n in [0..20]]; // Vincenzo Librandi, Jan 19 2018
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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