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%I #11 Feb 15 2019 05:39:54
%S 1,2,5,12,30,75,190,484,1242,3206,8316,21657,56591,148303,389615,
%T 1025810,2706014,7150411,18923033,50146688,133054093,353426693,
%U 939750924,2501100209,6662258807,17760491578,47381172431,126488492584
%N a(0)=1, a(n+1)=ceiling((1+1/n)^n*a(n)).
%H Harvey P. Dale, <a href="/A092247/b092247.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) is asymptotic to c*exp(n)/sqrt(n) where c=1.261(6)...
%F c = 1.2617447588213627326364194241966529846376230854758648215934468766256494736... - _Vaclav Kotesovec_, Feb 15 2019
%t nxt[{n_,a_}]:={n+1,Ceiling[(1+1/n)^n*a]}; Transpose[NestList[nxt,{1,1},30]][[2]] (* _Harvey P. Dale_, Oct 11 2012 *)
%o (PARI) a(n)=if(n<1,1,ceil((1+1/n)^n*a(n)))
%K nonn
%O 0,2
%A _Benoit Cloitre_, Feb 18 2004