A223897 - OEIS

%I #3 Mar 28 2013 21:05:09

%S 1,1,3,16,130,1485,22506,435027,10410920,301428809,10364922506,

%T 416904311679,19367862679116,1028066746575921,61777572340631590,

%U 4168811889484558531,313687075056806770384,26155857588261661013601,2403313718268521605455858,242132010466304405558972343

%N  E.g.f.: A(x) = Sum_{n>=0} 1/n! * Product_{k=1..n} -log(1 - sin(k*x)).

%e  E.g.f.: A(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 130*x^4/4! + 1485*x^5/5! +...

%e where

%e A(x) = 1 - log(1-sin(x)) + log(1-sin(x))*log(1-sin(2*x))/2! - log(1-sin(x))*log(1-sin(2*x))*log(1-sin(3*x))/3! + log(1-sin(x))*log(1-sin(2*x))*log(1-sin(3*x))*log(1-sin(4*x))/4! +...

%o  (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, prod(k=1, m, -log(1-sin(k*x+x*O(x^n))))/m!)); n!*polcoeff(A, n)}

%o for(n=0, 20, print1(a(n), ", "))

%Y  Cf. A223895, A223898.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 28 2013