login
E.g.f. exp(x)+log(1/(1-x)).
1

%I #30 Sep 08 2022 08:45:55

%S 1,2,2,3,7,25,121,721,5041,40321,362881,3628801,39916801,479001601,

%T 6227020801,87178291201,1307674368001,20922789888001,355687428096001,

%U 6402373705728001

%N E.g.f. exp(x)+log(1/(1-x)).

%C Apart from the offset, the same as A038507. - _R. J. Mathar_, Jun 07 2011

%H Vincenzo Librandi, <a href="/A185387/b185387.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = (n-1)!+1, n>0, a(0)=1.

%F From _Sergei N. Gladkovskii_, Jun 14 2012: (Start)

%F G.f. = 1 + x*G(0) where G(k) = 1 + k!/(1 - x/(x + (k!)/G(k+1))); (continued fraction, 3rd kind, 3-step).

%F E.g.f. = 1 + x*G(0)) where G(k)= 1 + k!/(1 - x/(x + (k+2)*(k!)/G(k+1))); (continued fraction, 3rd kind, 3-step).

%F (End).

%t Join[{1},Range[0,20]!+1] (* _Harvey P. Dale_, Jun 28 2011 *)

%o (PARI)

%o Vec(serlaplace(exp(x)+log(1/(1-x)))) [_Joerg Arndt_, Mar 03 2011]

%o (Magma) [1],[(1+Factorial(n-1)): n in [1..20]]; // _Vincenzo Librandi_, Oct 04 2011

%K nonn

%O 0,2

%A _Vladimir Kruchinin_, Feb 21 2011