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A177387 E.g.f.: Sum_{n>=0} Product_{k=1..n} sin(k*x).

%I A177387 #18 Nov 03 2014 07:31:37
%S A177387 1,1,4,35,536,12721,432364,19923455,1195597616,90597432961,
%T A177387 8459910749524,954441965659775,127987398340965896,
%U A177387 20120987017230590401,3665273670382984503484,765857737574513717138495
%N A177387 E.g.f.: Sum_{n>=0} Product_{k=1..n} sin(k*x).
%H A177387 Vaclav Kotesovec, <a href="/A177387/b177387.txt">Table of n, a(n) for n = 0..253</a>
%H A177387 Vaclav Kotesovec, <a href="/A177387/a177387.jpg">Graph of 1000 terms (limit to constant c)</a>
%F A177387 a(n) ~ c * 2^(n+1) * n^(2*n+7/6) / (Pi^(n-1) * exp(2*n) * (log(2))^n), where c = 1.01529686... . - _Vaclav Kotesovec_, Nov 03 2014
%e A177387 E.g.f: A(x) = 1 + x + 4*x^2/2! + 35*x^3/3! + 536*x^4/4! +...
%e A177387 A(x) = 1 + sin(x) + sin(x)*sin(2x) + sin(x)*sin(2x)*sin(3x) + ...
%t A177387 Flatten[{1,Rest[CoefficientList[Series[Sum[Product[Sin[m*x],{m,1,k}],{k,1,20}],{x,0,20}],x] * Range[0,20]!]}] (* _Vaclav Kotesovec_, Nov 03 2014 *)
%t A177387 nn=20; tab=ConstantArray[0,nn]; tab[[1]]=Series[Sin[x],{x,0,nn}]; Do[tab[[k]]=Series[tab[[k-1]]*Sin[k*x],{x,0,nn}],{k,2,nn}]; Flatten[{1,Rest[CoefficientList[Sum[tab[[k]],{k,1,nn}],x]*Range[0,nn]!]}] (* _Vaclav Kotesovec_, Nov 03 2014 (more efficient) *)
%o A177387 (PARI) {a(n)=local(X=x+x*O(x^n),Egf);Egf=sum(m=0,n,prod(k=1,m,sin(k*X)));n!*polcoeff(Egf,n)}
%Y A177387 Cf. A177388, A177385.
%K A177387 nonn,nice
%O A177387 0,3
%A A177387 _Paul D. Hanna_, May 15 2010