

A185387


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


1



1, 2, 2, 3, 7, 25, 121, 721, 5041, 40321, 362881, 3628801, 39916801, 479001601, 6227020801, 87178291201, 1307674368001, 20922789888001, 355687428096001, 6402373705728001
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OFFSET

0,2


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


FORMULA

a(n) = (n1)!+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, 3rd kind, 3step).
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, 3step).
(End).


MATHEMATICA

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


PROG

(PARI)
Vec(serlaplace(exp(x)+log(1/(1x)))) [Joerg Arndt, Mar 03 2011]
(MAGMA) [1], [(1+Factorial(n1)): n in [1..20]]; // Vincenzo Librandi, Oct 04 2011


CROSSREFS

Sequence in context: A076996 A139148 A293246 * A038507 A077001 A180996
Adjacent sequences: A185384 A185385 A185386 * A185388 A185389 A185390


KEYWORD

nonn


AUTHOR

Vladimir Kruchinin, Feb 21 2011


STATUS

approved



