OFFSET
0,3
COMMENTS
Compare e.g.f. to 1/(cosh(log(1-x)) + sinh(log(1-x))) = 1/(1-x).
LINKS
Amya Luo, Pattern Avoidance in Nonnesting Permutations, Undergraduate Thesis, Dartmouth College (2024). See p. 16.
FORMULA
a(n) ~ n! /(sqrt(2)*exp(Pi/4)*(1-exp(-Pi/4))^(n+1)). - Vaclav Kotesovec, Oct 18 2013
EXAMPLE
E.g.f.: A(x) = 1 + x + 4*x^2/2! + 22*x^3/3! + 162*x^4/4! + 1490*x^5/5! +...
where 1/A(1-exp(x)) = cos(x) + sin(x).
MATHEMATICA
CoefficientList[Series[1/(Cos[Log[1-x]] + Sin[Log[1-x]]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 18 2013 *)
PROG
(PARI) {a(n)=n!*polcoeff(1/(cos(log(1-x+x*O(x^n)))+sin(log(1-x+x*O(x^n)))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 21 2011
STATUS
approved