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 A168403 E.g.f.: Sum_{n>=0} sin(2^n*x)^n/n!. 3
 1, 2, 16, 504, 64512, 33226784, 68383997952, 561747553419136, 18430982918118572032, 2417076909966155927519744, 1267505531841541043488055885824, 2658351411163282144153185664555284480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) = [x^n/n! ] exp(2^n*sin(x)) for n>=0. EXAMPLE E.g.f.: A(x) = 1 + 2*x + 16*x^2/2! + 504*x^3/3! + 64512*x^4/4! +... 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! +... a(n) = coefficient of x^n/n! in G(x)^(2^n) where G(x) = exp(sin(x)): 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! +... PROG (PARI) {a(n)=n!*polcoeff(sum(k=0, n, sin(2^k*x +x*O(x^n))^k/k!), n)} (PARI) {a(n)=n!*polcoeff(exp(2^n*sin(x +x*O(x^n))), n)} CROSSREFS Cf. A002017 (exp(sin x)), variants: A168402, A136632. Sequence in context: A168402 A168406 A140310 * A140311 A012389 A009710 Adjacent sequences:  A168400 A168401 A168402 * A168404 A168405 A168406 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 25 2009 STATUS approved

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Last modified February 24 00:51 EST 2020. Contains 332195 sequences. (Running on oeis4.)