A185387 Expansion of e.g.f. exp(x)+log(1/(1-x)).

1, 2, 2, 3, 7, 25, 121, 721, 5041, 40321, 362881, 3628801, 39916801, 479001601, 6227020801, 87178291201, 1307674368001, 20922789888001, 355687428096001, 6402373705728001, 121645100408832001, 2432902008176640001, 51090942171709440001, 1124000727777607680001, 25852016738884976640001

Offset: 0

Author

Vladimir Kruchinin, Feb 21 2011

Keywords

• nonn

Comments

Apart from the offset, the same as A038507. - R. J. Mathar, Jun 07 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A038507.

Programs

Magma

[1] cat [(1+Factorial(n-1)): n in [1..20]]; // Vincenzo Librandi, Oct 04 2011

Mathematica

Join[{1},Range[0,20]!+1] (* Harvey P. Dale, Jun 28 2011 *)

PARI

Vec(serlaplace(exp(x)+log(1/(1-x)))) \\ Joerg Arndt, Mar 03 2011

Formula

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

From Sergei N. Gladkovskii, Jun 14 2012: (Start)

G.f.: 1 + x*G(0) where G(k) = 1 + k!/(1 - x/(x + (k!)/G(k+1))); (continued fraction).

E.g.f.: 1 + x*G(0) where G(k) = 1 + k!/(1 - x/(x + (k+2)*(k!)/G(k+1))); (continued fraction).

(End).