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%I #11 Aug 04 2015 12:34:26
%S 1,-1,5,-47,719,-16299,513253,-21430513,1145710573,-76317960163,
%T 6197399680779,-602640663660199,69134669061681469,
%U -9239224408001877873,1422887941494773642817,-250160794466824215921275,49797413478450579190546203,-11142367835115998962269070519,2784355004138005473128335461749
%N a(1)=1; a(n)=Sum_{k=1..n-1} Stirling_1(n,k)*a(k).
%C 2*Sum_{k>=1} a(k-1)/fallfac(n,k) = -1/n + Sum_{k>=1} (1 + a(k-1))/n^k, with the falling factorials fallfac(n,k) = Product_{j=0..k-1}(n-j). - _Vaclav Kotesovec_, Aug 04 2015
%H D. Barsky, J.-P. Bézivin, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Barsky/barsky5.html">p-adic Properties of Lengyel's Numbers</a>, Journal of Integer Sequences, 17 (2014), #14.7.3. See Y_n.
%F a(n) ~ (-1)^(n+1) * c * n!^2 / (n^(1-log(2)/3) * (2*log(2))^n), where c = A260932 = 0.9031646749584662473216609915945142350500875792441051556... . - _Vaclav Kotesovec_, Aug 04 2015
%p with(combinat);
%p Y:=proc(n) option remember; local k; if n=1 then 1 else add(stirling1(n,k)*Y(k),k=1..n-1); fi; end;
%p [seq(Y(n),n=1..35)];
%t Clear[a]; a[1] = 1; a[n_] := a[n] = Sum[StirlingS1[n, k]*a[k], {k, 1, n-1}]; Table[a[n], {n, 1, 20}] (* _Vaclav Kotesovec_, Aug 04 2015 *)
%Y A signed version of A086555.
%Y Cf. A005121, A260932.
%K sign
%O 1,3
%A _N. J. A. Sloane_, Aug 22 2014