OFFSET
0,4
COMMENTS
Sum_{n>=0} a(n)/n! = 4.
The radius of convergence of the e.g.f. is |x| <= 1.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: (1+x)^2 / (1-x^2)^(1-1/x).
a(n) ~ 15*(n-2)!/4 if n is even and a(n) ~ 17*(n-2)!/4 if n is odd. - Vaclav Kotesovec, Jun 02 2013
EXAMPLE
E.g.f.: A(x) = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 19*x^5/5! + 79*x^6/6! + 454*x^7/7! + 2673*x^8/8! + 20789*x^9/9! +...
where
log(A(x)) = x/(1*1) + x^3/(2*3) + x^5/(3*5) + x^7/(4*7) + x^9/(5*9) +...
MATHEMATICA
CoefficientList[Series[(1+x)^2/(1-x^2)^(1-1/x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 02 2013 *)
PROG
(PARI) {a(n)=n!*polcoeff(exp(sum(m=1, n, x^(2*m-1)/(m*(2*m-1)))+x*O(x^(2*n))), n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n)=n!*polcoeff( (1+x)^2 / (1-x^2 +x^2*O(x^n))^(1-1/x), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 14 2013
STATUS
approved