This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A144792 #18 Feb 25 2017 12:24:09
%S A144792 1,1,5,33,282,2938,36029,507440,8058990,142315830,2763775025,
%T A144792 58498072273,1339545500214,32980132065364,868417100538399,
%U A144792 24344702489881998,723694354351500431,22733368105181643193,752291980101845144878,26153153055424960528533
%N A144792 EXP transform of A140585.
%C A144792 Stirling transform of A143463.
%H A144792 Alois P. Heinz, <a href="/A144792/b144792.txt">Table of n, a(n) for n = 0..200</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); # _Alois P. Heinz_, Oct 10 2008
%t A144792 b[k_] := b[k] = DivisorSum[k, #/#!^(k/#)&]; c[n_] := c[n] = If[n==0, 1, Sum[(n-1)!/(n-k)!*b[k]*c[n-k], {k, 1, n}]]; aa[n_] := Sum[StirlingS2[n, k]*c[k], {k, 1, n}]; a[n_] := a[n] = If[n==0, 1, aa[n] + Sum[Binomial[ n-1, k-1]*aa[k]*a[n-k], {k, 1, n-1}]]; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Feb 25 2017, after _Alois P. Heinz_ *)
%Y A144792 Cf. A140585, A143463.
%K A144792 nonn
%O A144792 0,3
%A A144792 _Thomas Wieder_, Sep 21 2008
%E A144792 More terms from _Alois P. Heinz_, Oct 10 2008