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 A002776 Terms in certain determinants. (Formerly M3972 N1642) 2
 1, 5, 34, 258, 2136, 19320, 190800, 2051280, 23909760, 300827520, 4067884800, 58877280000, 908666035200, 14901260774400, 258832346572800, 4748165630208000, 91746433658880000, 1862735060938752000, 39649900359573504000, 883021783867711488000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 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 Muniru A Asiru, Table of n, a(n) for n = 0..100 J. D. H. Dickson, Discussion of two double series arising from the number of terms in determinants of certain forms, Proc. London Math. Soc., 10 (1879), 120-122. J. D. H. Dickson, Discussion of two double series arising from the number of terms in determinants of certain forms, Proc. London Math. Soc., 10 (1879), 120-122. [Annotated scanned copy] FORMULA 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 MAPLE A002776 := [seq(factorial(n+3) - 5 * factorial(n+2) + 6 * factorial(n+1) - factorial(n), n=0..100)]; # Muniru A Asiru, Jan 15 2018 MATHEMATICA Table[(n^3+n^2+2n+1)n!, {n, 0, 30}] (* Harvey P. Dale, Oct 28 2011 *) PROG (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 CROSSREFS Cf. A047922. Sequence in context: A080503 A078284 A083987 * A081342 A248055 A243659 Adjacent sequences:  A002773 A002774 A002775 * A002777 A002778 A002779 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Edited by Dean Hickerson, Sep 20 2002 STATUS approved

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Last modified January 20 14:40 EST 2019. Contains 319333 sequences. (Running on oeis4.)