A223895 E.g.f.: A(x) = Sum_{n>=0} 1/n! * Product_{k=1..n} -log(1 - sinh(k*x)).

1, 1, 3, 18, 178, 2565, 50266, 1281189, 41079928, 1614373833, 76159289386, 4240914224481, 274875377524804, 20493884997114945, 1739962105428020566, 166758905926021916373, 17904330331671454817392, 2139078334935145657604961, 282684498251824376254841266

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 18*x^3/3! + 178*x^4/4! + 2565*x^5/5! +...
where
A(x) = 1 - log(1-sinh(x)) + log(1-sinh(x))*log(1-sinh(2*x))/2! - log(1-sinh(x))*log(1-sinh(2*x))*log(1-sinh(3*x))/3! + log(1-sinh(x))*log(1-sinh(2*x))*log(1-sinh(3*x))*log(1-sinh(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-sinh(k*x+x*O(x^n))))/m!)); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A223896, A223897.

Sequence in context: A365600 A080687 A231619 * A111465 A247029 A108994

Adjacent sequences: A223892 A223893 A223894 * A223896 A223897 A223898

Keyword

nonn

Author

Paul D. Hanna, Mar 28 2013

Status

approved