A198201 G.f.: q-cosh(x) evaluated at q=-x.

1, 0, 1, 1, 2, 4, 6, 9, 14, 18, 18, 16, 67, 67, 66, 72, 84, 99, 117, 138, 159, 468, 516, 578, 679, 810, 933, 1018, 1072, 1138, 1262, 1448, 4745, 5196, 5851, 6630, 7382, 8031, 8649, 9405, 10409, 11569, 12649, 13530, 14378, 51022, 55567, 60439, 65906, 71953, 78283

Offset: 0

Author

Paul D. Hanna, Aug 07 2012

Keywords

• nonn

Comments

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

Examples

			 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 +...
		

Crossrefs

Cf. A152398 (e_q), A198197 (E_q), A198242 (q-Cosh), A198243 (q-Sinh), A198202 (q-sinh).

Cf. A198199, A198200.

Programs

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),", "))

Formula

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