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A223897
E.g.f.: A(x) = Sum_{n>=0} 1/n! * Product_{k=1..n} -log(1 - sin(k*x)).
2
1, 1, 3, 16, 130, 1485, 22506, 435027, 10410920, 301428809, 10364922506, 416904311679, 19367862679116, 1028066746575921, 61777572340631590, 4168811889484558531, 313687075056806770384, 26155857588261661013601, 2403313718268521605455858, 242132010466304405558972343
OFFSET
0,3
EXAMPLE
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 130*x^4/4! + 1485*x^5/5! +...
where
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! +...
PROG
(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)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
Sequence in context: A135752 A218827 A120021 * A131490 A121673 A273997
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 28 2013
STATUS
approved