cp's OEIS Frontend

A177388 O.g.f.: Sum_{n>=0} Product_{k=1..n} sin(k*arcsin(2x)).

%I A177388 #8 Jan 17 2018 03:16:28
%S A177388 1,2,8,48,368,3488,39408,517536,7747552,130224448,2428303280,
%T A177388 49745334816,1110519910176,26832869319872,697671946188128,
%U A177388 19422303020653632,576390053072381888,18164695560213480064
%N A177388 O.g.f.: Sum_{n>=0} Product_{k=1..n} sin(k*arcsin(2x)).
%H A177388 Vaclav Kotesovec, <a href="/A177388/b177388.txt">Table of n, a(n) for n = 0..260</a>
%F A177388 O.g.f.: A(x) = G(arcsin(2x)) where G(x) = e.g.f. of A177387.
%F A177388 a(n) ~ c * (4/(Pi*log(2)))^n * n! * n^(1/6), where c = 1.01529686... . - _Vaclav Kotesovec_, Nov 04 2014
%e A177388 O.g.f.: A(x) = 1 + 2*x + 8*x^2 + 48*x^3 + 368*x^4 + 3488*x^5 + ...
%e A177388 Let G(x) be the e.g.f. of A177387:
%e A177388 G(x) = 1 + x + 4*x^2/2! + 35*x^3/3! + 536*x^4/4! + ...
%e A177388 then A(x) = G(arcsin(2*x)).
%o A177388 (PARI) {a(n)=local(X=x+x*O(x^n),Ogf);Ogf=sum(m=0,n,prod(k=1,m,sin(k*asin(2*X))));polcoeff(Ogf,n)}
%Y A177388 Cf. A177387.
%K A177388 nonn
%O A177388 0,2
%A A177388 _Paul D. Hanna_, May 15 2010