cp's OEIS Frontend

A168403 E.g.f.: Sum_{n>=0} sin(2^n*x)^n/n!.

%I A168403 #5 Oct 11 2020 04:05:50
%S A168403 1,2,16,504,64512,33226784,68383997952,561747553419136,
%T A168403 18430982918118572032,2417076909966155927519744,
%U A168403 1267505531841541043488055885824,2658351411163282144153185664555284480
%N A168403 E.g.f.: Sum_{n>=0} sin(2^n*x)^n/n!.
%F A168403 a(n) = [x^n/n! ] exp(2^n*sin(x)) for n>=0.
%F A168403 a(n) ~ 2^(n^2). - _Vaclav Kotesovec_, Oct 11 2020
%e A168403 E.g.f.: A(x) = 1 + 2*x + 16*x^2/2! + 504*x^3/3! + 64512*x^4/4! +...
%e A168403 A(x) = 1 + sin(2*x) + sin(4*x)^2/2! + sin(8*x)^3/3! + sin(16*x)^4/4! +...+ sin(2^n*x)^n/n! +...
%e A168403 a(n) = coefficient of x^n/n! in G(x)^(2^n) where G(x) = exp(sin(x)):
%e A168403 G(x) = 1 + x + x^2/2! - 3*x^4/4! - 8*x^5/5! - 3*x^6/6! + 56*x^7/7! +...+ A002017(n)*x^n/n! +...
%t A168403 nmax = 12; CoefficientList[Series[Sum[Sin[2^k*x]^k/k!, {k, 0, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Oct 11 2020 *)
%o A168403 (PARI) {a(n)=n!*polcoeff(sum(k=0,n,sin(2^k*x +x*O(x^n))^k/k!),n)}
%o A168403 (PARI) {a(n)=n!*polcoeff(exp(2^n*sin(x +x*O(x^n))),n)}
%Y A168403 Cf. A002017 (exp(sin x)), variants: A168402, A136632.
%K A168403 nonn
%O A168403 0,2
%A A168403 _Paul D. Hanna_, Nov 25 2009