cp's OEIS Frontend

A168406 E.g.f.: Sum_{n>=0} arctan(2^n*x)^n/n!.

%I A168406 #5 Jan 15 2018 15:34:34
%S A168406 1,2,16,496,63488,32899840,68049141760,560546415810560,
%T A168406 18415229458563727360,2416302337337071616327680,
%U A168406 1267360474688679165942982246400,2658246833688954938616062542151680000
%N A168406 E.g.f.: Sum_{n>=0} arctan(2^n*x)^n/n!.
%F A168406 a(n) = [x^n/n!] exp(2^n*arctan(x)) for n >= 0.
%e A168406 E.g.f.: A(x) = 1 + 2*x + 16*x^2/2! + 496*x^3/3! + 63488*x^4/4! + ...
%e A168406 A(x) = 1 + arctan(2*x) + arctan(4*x)^2/2! + arctan(8*x)^3/3! + arctan(16*x)^4/4! + ... + arctan(2^n*x)^n/n! + ...
%e A168406 a(n) = coefficient of x^n/n! in G(x)^(2^n) where G(x) = exp(arctan(x)):
%e A168406 G(x) = 1 + x + x^2/2! - x^3/3! - 7*x^4/4! + 5*x^5/5! + 145*x^6/6! + ... + A002019(n)*x^n/n! + ...
%o A168406 (PARI) {a(n)=n!*polcoeff(sum(k=0,n,atan(2^k*x +x*O(x^n))^k/k!),n)}
%o A168406 (PARI) {a(n)=n!*polcoeff(exp(2^n*atan(x +x*O(x^n))),n)}
%Y A168406 Cf. A002019 (exp(arctan x)), variants: A136632, A168402, A168403, A168404, A168405, A168407, A168408.
%K A168406 nonn
%O A168406 0,2
%A A168406 _Paul D. Hanna_, Nov 25 2009