cp's OEIS Frontend

A193263 G.f.: A(x) = x + Sum_{n>=1} x^(2*n) / (1+x)^A193259(n).

%I A193263 #15 Mar 30 2012 18:37:28
%S A193263 1,1,-1,2,-5,12,-26,52,-101,201,-422,927,-2070,4579,-9894,20789,
%T A193263 -42517,84937,-166570,322700,-622500,1207056,-2376168,4787523,
%U A193263 -9908610,21021499,-45404102,98952388,-215756156,467541948,-1002478352,2121546013,-4427208709,9110572776,-18503242145,37135048484,-73759839074
%N A193263 G.f.: A(x) = x + Sum_{n>=1} x^(2*n) / (1+x)^A193259(n).
%C A193263 Note: A193259(n) = n + floor(log_2(n)) + A011371(n), where A011371(n) = highest power of 2 dividing n!.
%C A193263 The g.f. A(x), as a power series in x, diverges at x=-1/2 and converges at x=+1/2 to A(1/2) = 0.6811907120229079095390167697...
%C A193263 Other values: A(x) = 1/2 at x = 0.385874434537804442263..., A(x) = 1 at x = 0.685568171776262105563..., A((sqrt(5)-1)/2) = 0.880771363850914609641...
%F A193263 G.f.: A(x) = Sum_{n>=1} x^n / (1+x)^(A193259(n) - n).
%e A193263 G.f.: A(x) = x + x^2 - x^3 + 2*x^4 - 5*x^5 + 12*x^6 - 26*x^7 + 52*x^8 +...
%e A193263 where
%e A193263 A(x) = x + x^2/(1+x)^1 + x^4/(1+x)^4 + x^6/(1+x)^5 + x^8/(1+x)^9 + x^10/(1+x)^10 + x^12/(1+x)^12 + x^14/(1+x)^13 + x^16/(1+x)^18 +...+ x^(2*n)/(1+x)^A193259(n) +...
%e A193263 Also,
%e A193263 A(x) = x/(1+x)^0 + x^2/(1+x)^2 + x^3/(1+x)^2 + x^4/(1+x)^5 + x^5/(1+x)^5 + x^6/(1+x)^6 + x^7/(1+x)^6 + x^8/(1+x)^10 +...+ x^n/(1+x)^(A193259(n)-n) +...
%o A193263 (PARI) {a(n)=polcoeff(sum(m=1,n,x^m/(1+x+x*O(x^n))^(floor(log(m+1/2)/log(2)) + valuation(m!, 2))),n)}
%Y A193263 Cf. A193259, A011371, A000523.
%K A193263 sign
%O A193263 1,4
%A A193263 _Paul D. Hanna_, Jul 19 2011