OFFSET
0,3
FORMULA
E.g.f.: log(1+sin(x)/exp(x)).
a(n) = 2*Sum_(k=1..n, Sum_(j=0..(n-k)/2, C(n,n-k-2*j)*(k^(n-k-2*j) *Sum_(i=0..k/2, (2*i-k)^(k+2*j)*C(k,i)*(-1)^(k+j-i))))/(2^k*k)). - Vladimir Kruchinin, Jun 13 2011
a(n) ~ (-1)^(n+1) * (n-1)! / r^n, where r = 0.588532743981861... is the real root of the equation sin(r) = exp(-r). - Vaclav Kotesovec, Oct 25 2013
MATHEMATICA
CoefficientList[Series[Log[1+Sin[x]/Exp[x]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 25 2013 *)
PROG
(Maxima)
a(n):=2*sum(sum(binomial(n, n-k-2*j)*(k^(n-k-2*j)*sum((2*i-k)^(k+2*j) *binomial(k, i)*(-1)^(k+j-i), i, 0, k/2)), j, 0, (n-k)/2)/(2^k*k), k, 1, n); [Vladimir Kruchinin, Jun 13 2011]
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
STATUS
approved