A198242 G.f.: q-Cosh(x) evaluated at q=-x.

1, 0, 0, -1, -1, -1, -1, -1, -1, -1, 0, 2, 3, 2, 1, 2, 4, 5, 5, 5, 5, 4, 1, -3, -5, -4, -2, -1, -3, -9, -15, -16, -14, -15, -21, -29, -33, -26, -7, 12, 14, -3, -21, -22, -7, 9, 16, 17, 20, 31, 52, 75, 84, 76, 72, 92, 124, 131, 91, 27, -8, 18, 83, 132, 127, 81, 46, 55

Offset: 0

Author

Paul D. Hanna, Aug 07 2012

Keywords

• sign

Comments

Note: q-Cosh(x) = Sum_{n>=0} x^(2*n) * q^(n*(2*n-1)) / Product_{k=1..2*n} (1-q^k)/(1-q).

Examples

			G.f.: 1 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8 - x^9 + 2*x^11 + 3*x^12 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A152398 (e_q), A198197 (E_q), A198243 (q-Sinh), A198201 (q-cosh), A198202 (q-sinh).

Cf. A198199, A198200.

Programs

PARI

{a(n)=local(Cosh_q=sum(k=0, sqrtint(n+4), (-x)^(k*(2*k-1))*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),", "))

Formula

G.f.: Sum_{n>=0} x^(2*n) * (-x)^(n*(2*n-1)) / Product_{k=1..2*n} (1-(-x)^k)/(1+x).