cp's OEIS Frontend

A168405 E.g.f.: Sum_{n>=0} arcsin(2^n*x)^n/n!.

%I A168405 #5 Jan 17 2018 03:24:46
%S A168405 1,2,16,520,66560,33882400,69055283200,564153087455360,
%T A168405 18462510039810703360,2418626471936038215754240,
%U A168405 1267795676362601991645220044800,2658560574070850656450883768752998400
%N A168405 E.g.f.: Sum_{n>=0} arcsin(2^n*x)^n/n!.
%F A168405 a(n) = [x^n/n!] exp(2^n*arcsin(x)) for n >= 0.
%e A168405 E.g.f.: A(x) = 1 + 2*x + 16*x^2/2! + 520*x^3/3! + 66560*x^4/4! + ...
%e A168405 A(x) = 1 + arcsin(2*x) + arcsin(4*x)^2/2! + arcsin(8*x)^3/3! + arcsin(16*x)^4/4! + ... + arcsin(2^n*x)^n/n! + ...
%e A168405 a(n) = coefficient of x^n/n! in G(x)^(2^n) where G(x) = exp(arcsin(x)):
%e A168405 G(x) = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 20*x^5/5! + 85*x^6/6! + ... + A006228(n)*x^n/n! + ...
%o A168405 (PARI) {a(n)=n!*polcoeff(sum(k=0,n,asin(2^k*x +x*O(x^n))^k/k!),n)}
%o A168405 (PARI) {a(n)=n!*polcoeff(exp(2^n*asin(x +x*O(x^n))),n)}
%Y A168405 Cf. A006228 (exp(arcsin x)), variants: A136632, A168402, A168403, A168404, A168406, A168407, A168408.
%K A168405 nonn
%O A168405 0,2
%A A168405 _Paul D. Hanna_, Nov 25 2009