OFFSET
1,4
COMMENTS
Note: q-sinh(x) = Sum_{n>=0} x^(2*n+1) / Product_{k=1..2*n+1} (1-q^k)/(1-q).
FORMULA
G.f.: Sum_{n>=0} x^(2*n+1) / Product_{k=1..2*n+1} (1-(-x)^k)/(1+x).
EXAMPLE
G.f.: x + x^3 + 2*x^4 + 3*x^5 + 5*x^6 + 8*x^7 + 13*x^8 + 22*x^9 + 31*x^10 +...
PROG
(PARI) {a(n)=local(Sinh_q=sum(k=0, sqrtint(n+4), x^(2*k+1)/(prod(j=1, 2*k+1, (1-(-x)^j)/(1+x))+x*O(x^n)))); polcoeff(Sinh_q, n)}
for(n=0, 81, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 07 2012
STATUS
approved