A223897 E.g.f.: A(x) = Sum_{n>=0} 1/n! * Product_{k=1..n} -log(1 - sin(k*x)).

1, 1, 3, 16, 130, 1485, 22506, 435027, 10410920, 301428809, 10364922506, 416904311679, 19367862679116, 1028066746575921, 61777572340631590, 4168811889484558531, 313687075056806770384, 26155857588261661013601, 2403313718268521605455858, 242132010466304405558972343

Offset

0,3

Links

Table of n, a(n) for n=0..19.

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

Cf. A223895, A223898.

Sequence in context: A135752 A218827 A120021 * A131490 A121673 A273997

Adjacent sequences: A223894 A223895 A223896 * A223898 A223899 A223900

Keyword

nonn

Author

Paul D. Hanna, Mar 28 2013

Status

approved