OFFSET
0,5
COMMENTS
Note: q-cosh(x) = Sum_{n>=0} x^(2*n) / Product_{k=1..2*n} (1-q^k)/(1-q).
FORMULA
G.f.: Sum_{n>=0} x^(2*n) / Product_{k=1..2*n} (1-(-x)^k)/(1+x).
EXAMPLE
G.f.: 1 + x^2 + x^3 + 2*x^4 + 4*x^5 + 6*x^6 + 9*x^7 + 14*x^8 + 18*x^9 +...
PROG
(PARI) {a(n)=local(Cosh_q=sum(k=0, sqrtint(n+4), x^(2*k)/(prod(j=1, 2*k, (1-(-x)^j)/(1+x)+x*O(x^n))))); polcoeff(Cosh_q, n)}
for(n=0, 81, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 07 2012
STATUS
approved