cp's OEIS Frontend

A110152 G.f.: A(x) = Product_{n>=1} 1/(1 - 2^n*x^n)^(2/2^n).

%I A110152 #10 Oct 18 2020 07:50:29
%S A110152 1,2,6,14,36,78,192,406,942,2018,4512,9450,21178,43950,95532,200398,
%T A110152 431356,892518,1917572,3950614,8410230,17398466,36648980,75326754,
%U A110152 159199004,326471706,683028924,1404145162,2930071798,5993625942
%N A110152 G.f.: A(x) = Product_{n>=1} 1/(1 - 2^n*x^n)^(2/2^n).
%H A110152 Vaclav Kotesovec, <a href="/A110152/b110152.txt">Table of n, a(n) for n = 0..1000</a>
%F A110152 G.f.: exp( Sum_{n>=1} 2*A090879(n)*x^n/n ), where A090879(n) = Sum_{d|n} d*2^(n-d). - _Paul D. Hanna_, Jan 05 2014
%e A110152 G.f.: A(x) = 1 + 2*x + 6*x^2 + 14*x^3 + 36*x^4 + 78*x^5 +...
%e A110152 where
%e A110152 A(x) = 1/((1-2*x) * (1-4*x^2)^(1/2) * (1-8*x^3)^(1/4) * (1-16*x^4)^(1/8) *...).
%t A110152 nmax = 30; CoefficientList[Series[Product[1/(1 - 2^k*x^k)^(2/2^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 18 2020 *)
%o A110152 (PARI) a(n)=polcoeff(prod(k=1,n,1/(1-2^k*x^k+x*O(x^n))^(2/2^k)),n)
%o A110152 (PARI) A090879(n) = sumdiv(n,d, d*2^(n-d))
%o A110152 a(n)=local(A);A=exp(sum(k=1,n,2*A090879(k)*x^k/k)+x*O(x^n));polcoeff(A,n)
%o A110152 for(n=0,30,print1(a(n),", ")) \\ _Paul D. Hanna_, Jan 05 2014
%Y A110152 Cf. A110153, A110154, A110155, A110156.
%K A110152 nonn
%O A110152 0,2
%A A110152 _Paul D. Hanna_, Jul 14 2005