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%I #3 Aug 07 2012 02:25:49
%S 1,0,1,1,2,4,6,9,14,18,18,16,67,67,66,72,84,99,117,138,159,468,516,
%T 578,679,810,933,1018,1072,1138,1262,1448,4745,5196,5851,6630,7382,
%U 8031,8649,9405,10409,11569,12649,13530,14378,51022,55567,60439,65906,71953,78283
%N G.f.: q-cosh(x) evaluated at q=-x.
%C Note: q-cosh(x) = Sum_{n>=0} x^(2*n) / Product_{k=1..2*n} (1-q^k)/(1-q).
%F G.f.: Sum_{n>=0} x^(2*n) / Product_{k=1..2*n} (1-(-x)^k)/(1+x).
%e 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 +...
%o (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)}
%o for(n=0,81,print1(a(n),", "))
%Y Cf. A152398 (e_q), A198197 (E_q), A198242 (q-Cosh), A198243 (q-Sinh), A198202 (q-sinh).
%Y Cf. A198199, A198200.
%K nonn
%O 0,5
%A _Paul D. Hanna_, Aug 07 2012
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