A177388 - OEIS

%I #8 Jan 17 2018 03:16:28

%S 1,2,8,48,368,3488,39408,517536,7747552,130224448,2428303280,

%T 49745334816,1110519910176,26832869319872,697671946188128,

%U 19422303020653632,576390053072381888,18164695560213480064

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

%H Vaclav Kotesovec, <a href="/A177388/b177388.txt">Table of n, a(n) for n = 0..260</a>

%F O.g.f.: A(x) = G(arcsin(2x)) where G(x) = e.g.f. of A177387.

%F a(n) ~ c * (4/(Pi*log(2)))^n * n! * n^(1/6), where c = 1.01529686... . - _Vaclav Kotesovec_, Nov 04 2014

%e O.g.f.: A(x) = 1 + 2*x + 8*x^2 + 48*x^3 + 368*x^4 + 3488*x^5 + ...

%e Let G(x) be the e.g.f. of A177387:

%e G(x) = 1 + x + 4*x^2/2! + 35*x^3/3! + 536*x^4/4! + ...

%e then A(x) = G(arcsin(2*x)).

%o (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 Cf. A177387.

%K nonn

%O 0,2

%A _Paul D. Hanna_, May 15 2010