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A110448 G.f.: A(x) = exp( Sum_{n>=1} A056045(n)/n*x^n ), where A056045(n) = Sum_{d|n} binomial(n,d).

%I A110448 #14 Jan 15 2019 08:18:27
%S A110448 1,1,2,3,6,8,18,23,49,73,145,194,474,611,1331,2027,4393,5919,14736,
%T A110448 19415,46487,68504,156618,212055,560380,739165,1833012,2657837,
%U A110448 6513367,8743208,23649777,31140300,81276046,114962333,293600318,391926154
%N A110448 G.f.: A(x) = exp( Sum_{n>=1} A056045(n)/n*x^n ), where A056045(n) = Sum_{d|n} binomial(n,d).
%H A110448 Seiichi Manyama, <a href="/A110448/b110448.txt">Table of n, a(n) for n = 0..3337</a>
%F A110448 G.f.: A(x) = Product_{n>=1} (1/x)*Series_Reversion( x/(1 + x^n) ); equivalently, G.f.: A(x) = Product_{n>=1} G(x^n,n) where G(x,n) = 1 + x*G(x,n)^n.
%F A110448 a(n) ~ c * 2^n / n^(3/2), where c = 2.8176325363130737043447... if n is even and c = 1.784372019603712867208... if n is odd. - _Vaclav Kotesovec_, Jan 15 2019
%e A110448 G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 8*x^5 + 18*x^6 +...
%e A110448 where A(x) = exp( Sum_{n>=1} A056045(n)/n*x^n ), or
%e A110448 A(x) = exp(x + 3/2*x^2 + 4/3*x^3 + 11/4*x^4 + 6/5*x^5 +...).
%e A110448 The g.f. can also be expressed as the product:
%e A110448 A(x) = 1/(1-x)*G000108(x^2)*G001764(x^3)*G002293(x^4)*G002294(x^5)*...
%e A110448 where the functions are g.f.s of well-known sequences:
%e A110448 G000108(x) = 1 + x*G000108(x)^2 = g.f. of A000108 ;
%e A110448 G001764(x) = 1 + x*G001764(x)^3 = g.f. of A001764 ;
%e A110448 G002293(x) = 1 + x*G002293(x)^4 = g.f. of A002293 ;
%e A110448 G002294(x) = 1 + x*G002294(x)^5 = g.f. of A002294 ; etc.
%o A110448 (PARI) {a(n)=polcoeff(exp(x*Ser(vector(n,m, sumdiv(m,d,binomial(m,d))/m))+x*O(x^n)),n)}
%o A110448 (PARI) {a(n)=polcoeff(prod(m=1,n,1/x*serreverse(x/(1+x^m +x*O(x^n)))),n)}
%Y A110448 Cf. A056045, A174461, A206290.
%Y A110448 Cf. A000108, A001764, A002293, A002294, A002295.
%K A110448 nonn
%O A110448 0,3
%A A110448 _Paul D. Hanna_, Jul 20 2005, Nov 10 2007