|
%I #21 May 09 2023 08:32:29
%S -1,1,1,7,35,221,1589,12979,118663,1201465,13349609,161530271,
%T 2114578091,29780308117,448995414685,7215997736011,123153028027919,
%U 2224451568754289,42395429898611153,850263899633257015,17900292623858042419,394701452356069835341
%N First differences of A000166.
%H G. C. Greubel, <a href="/A105926/b105926.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = n*!n - (-1)^n, where !n = A000166(n) is subfactorial. - _Vladimir Reshetnikov_, Nov 03 2015
%F (2n + 1) a(n+2) = (2n^2 + 5n + 4) a(n+1) + (2n^2 + 5n + 3) a(n). E.g.f.: exp(-x)*(2*x-1)/(x-1)^2. - _Robert Israel_, Nov 03 2015
%p a:=n->sum((-1)^k * (n-k-1) * n!/k!, k=0..n): seq(a(n), n=0..20); # _Zerinvary Lajos_, Jun 27 2007
%p A000166:= gfun:-rectoproc({a(0)=1,a(1)=0,a(n) = (n-1)*(a(n-1)+a(n-2))},a(n),remember):
%p seq(A000166(n+1)-A000166(n),n=0..100); # _Robert Israel_, Nov 03 2015
%t Table[Subfactorial[n] - Subfactorial[n - 1], {n, 1, 22}] (* _Zerinvary Lajos_, Jul 09 2009 *)
%t Table[n Subfactorial[n] - (-1)^n, {n, 0, 20}] (* _Vladimir Reshetnikov_, Nov 01 2015 *)
%t Differences[Table[(-1)^n HypergeometricPFQ[{-n,1},{},1], {n,0,20}]] (* _Peter Luschny_, Nov 03 2015 *)
%Y Cf. A000166.
%K sign
%O 0,4
%A _N. J. A. Sloane_, Apr 27 2005
|
