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A177386 O.g.f.: Sum_{n>=0} Product_{k=1..n} sinh(k*arcsinh(2x)).

%I A177386 #13 Jul 22 2018 08:46:45
%S A177386 1,2,8,48,400,4192,52720,773536,12970016,244625088,5125896112,
%T A177386 118137655840,2970016739552,80883641686848,2372035401856352,
%U A177386 74528583049288768,2497667361588205632,88932255196677684608
%N A177386 O.g.f.: Sum_{n>=0} Product_{k=1..n} sinh(k*arcsinh(2x)).
%C A177386 Lim_{n->infinity} n!*A177386(n) / (2^n*A177385(n)) = 1. - _Vaclav Kotesovec_, Nov 06 2014
%H A177386 Vaclav Kotesovec, <a href="/A177386/b177386.txt">Table of n, a(n) for n = 0..200</a>
%F A177386 O.g.f.: A(x) = G(arcsinh(2x)) where G(x) = e.g.f. of A177385.
%F A177386 a(n) ~ c * d^n * n!, where d = 2*A249748 = 2.0937983852519084822268503..., c = 0.880333778211172907563073... (constant c is same as for A177385). - _Vaclav Kotesovec_, Nov 06 2014
%e A177386 O.g.f.: A(x) = 1 + 2*x + 8*x^2 + 48*x^3 + 400*x^4 + 4192*x^5 + ...
%e A177386 Let G(x) be the e.g.f. of A177385:
%e A177386 G(x) = 1 + x + 4*x^2/2! + 37*x^3/3! + 616*x^4/4! + 16081*x^5/5! + ...
%e A177386 then A(x) = G(arcsinh(2x)).
%o A177386 (PARI) {a(n)=local(X=x+x*O(x^n),Egf);Egf=sum(m=0,n,prod(k=1,m,sinh(k*asinh(2*X))));polcoeff(Egf,n)}
%Y A177386 Cf. A177385, A249748.
%K A177386 nonn
%O A177386 0,2
%A A177386 _Paul D. Hanna_, May 15 2010