cp's OEIS Frontend

A156100 G.f.: A(x) = exp( Sum_{n>=1} (1 + 2^n*x)^n * x^n/n ).

%I A156100 #9 Oct 17 2020 05:02:42
%S A156100 1,1,3,7,25,113,741,7181,101139,2089283,61683087,2600572391,
%T A156100 156100460443,13231060891179,1594932996895155,270715422001769667,
%U A156100 65209448673400087945,22130613779988110245993,10631829612570393072035829,7207580557759524950136903565,6902254922678483464065364019049,9340558535943272871301176019398265,17831418294195720284498112713266643601
%N A156100 G.f.: A(x) = exp( Sum_{n>=1} (1 + 2^n*x)^n * x^n/n ).
%C A156100 Compare to g.f. exp( Sum_{m>=1} (1 + x)^m * x^m/m ) of the Fibonacci sequence.
%C A156100 Conjecture: a(n)^(1/n^2) tends to 2^(1/4). - _Vaclav Kotesovec_, Oct 17 2020
%H A156100 Paul D. Hanna, <a href="/A156100/b156100.txt">Table of n, a(n) for n = 0..150</a>
%F A156100 G.f.: A(x) = exp(F(x)) where F(x) is the l.g.f. of A156101.
%e A156100 G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 25*x^4 + 113*x^5 + 741*x^6 +...
%e A156100 log(A(x)) = (1 + 2*x)*x + (1 + 2^2*x)^2*x^2/2 + (1 + 2^3*x)^3*x^3/3 +...
%e A156100 log(A(x)) = x + 5*x^2/2 + 13*x^3/3 + 65*x^4/4 + 401*x^5/5 + 3521*x^6/6 +...
%o A156100 (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,(1+2^m*x)^m*x^m/m)+x*O(x^n)),n)}
%o A156100 for(n=0,25,print1(a(n),", "))
%Y A156100 Cf. A156101 (log), A155810.
%K A156100 nonn
%O A156100 0,3
%A A156100 _Paul D. Hanna_, Feb 04 2009