login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
E.g.f.: (1 + x + 3*x^2 + x^3)/(1 - x)^4. - Stefano Spezia, Apr 17 2022
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 * A333804 A081342 A248055
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Edited by Dean Hickerson, Sep 20 2002
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 02:46 EDT 2024. Contains 370952 sequences. (Running on oeis4.)