%I A144792
%S A144792 1,5,33,282,2938,36029,507440,8058990,142315830,2763775025,58498072273,
%T A144792 1339545500214,32980132065364,868417100538399,24344702489881998,
%U A144792 723694354351500431,22733368105181643193,752291980101845144878
%N A144792 EXP transform of A140585.
%C A144792 Stirling transform of A143463.
%H A144792 Thomas Wieder, <a href="http://www.thomas-wieder.privat.t-online.de/default.html">
               Home Page</a>.
%H A144792 Thomas Wieder, <a href="http://homepages.tu-darmstadt.de/~wieder/Welcome.html">
               (Old) Home Page</a>.
%F A144792 E.g.f: (1/exp(1)) exp( 1 / prod_{k=1}^{inf} (1 - (exp(x)-1)^k / k!) ).
%F A144792 a(n) = sum_{k=1}^{n} C(n-1,k-1) A140585(k) a(n-k).
%F A144792 With S2(n,k) as the Stirling number of the second kind we have
%F A144792 a(n) = sum_{k=1}^{n} A143463(n) S2(n,k).
%p A144792 with (numtheory): with (combinat): b:= proc(k) option remember; add (d/
               d!^(k/d), d=divisors(k)) end: c:= proc(n) option remember; `if` (n=0, 
               1, add ((n-1)!/ (n-k)!* b(k)* c(n-k), k=1..n)) end: aa:= n-> add 
               (stirling2 (n, k) * c(k), k=1..n): a:= proc(n) option remember; `if` 
               (n=0, 1, aa(n)+ add (binomial (n-1, k-1) *aa(k) *a(n-k), k=1..n-1)) 
               end: seq (a(n), n=1..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Oct 10 2008]
%Y A144792 A140585, A143463.
%Y A144792 Sequence in context: A049377 A129890 A120733 this_sequence A001828 A084845 
               A098460
%Y A144792 Adjacent sequences: A144789 A144790 A144791 this_sequence A144793 A144794 
               A144795
%K A144792 nonn
%O A144792 1,2
%A A144792 Thomas Wieder (thomas.wieder(AT)t-online.de), Sep 21 2008
%E A144792 More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 10 2008