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%I M3972 N1642 #43 Apr 17 2022 10:24:08
%S 1,5,34,258,2136,19320,190800,2051280,23909760,300827520,4067884800,
%T 58877280000,908666035200,14901260774400,258832346572800,
%U 4748165630208000,91746433658880000,1862735060938752000,39649900359573504000,883021783867711488000
%N Terms in certain determinants.
%C 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
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Muniru A Asiru, <a href="/A002776/b002776.txt">Table of n, a(n) for n = 0..100</a>
%H J. D. H. Dickson, <a href="https://doi.org/10.1112/plms/s1-10.1.120">Discussion of two double series arising from the number of terms in determinants of certain forms</a>, Proc. London Math. Soc., 10 (1879), 120-122.
%H J. D. H. Dickson, <a href="/A002775/a002775.pdf">Discussion of two double series arising from the number of terms in determinants of certain forms</a>, Proc. London Math. Soc., 10 (1879), 120-122. [Annotated scanned copy]
%F a(n) = (n^3 + n^2 + 2*n + 1)*n!.
%F a(n) = (n+3)! - 5*(n+2)! + 6*(n+1)! - n!. - _Umut Özer_, Dec 26 2017
%F E.g.f.: (1 + x + 3*x^2 + x^3)/(1 - x)^4. - _Stefano Spezia_, Apr 17 2022
%p A002776 := [seq(factorial(n+3) - 5 * factorial(n+2) + 6 * factorial(n+1) - factorial(n), n=0..100)]; # _Muniru A Asiru_, Jan 15 2018
%t Table[(n^3+n^2+2n+1)n!,{n,0,30}] (* _Harvey P. Dale_, Oct 28 2011 *)
%o (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
%o (Magma) [(n^3+n^2+2*n+1)*Factorial(n): n in [0..20]]; // _Vincenzo Librandi_, Jan 19 2018
%Y Cf. A047922.
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_
%E Edited by _Dean Hickerson_, Sep 20 2002
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