cp's OEIS Frontend

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

%I A198242 #5 May 10 2013 18:12:13
%S A198242 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,
%T A198242 -3,-9,-15,-16,-14,-15,-21,-29,-33,-26,-7,12,14,-3,-21,-22,-7,9,16,17,
%U A198242 20,31,52,75,84,76,72,92,124,131,91,27,-8,18,83,132,127,81,46,55
%N A198242 G.f.: q-Cosh(x) evaluated at q=-x.
%C A198242 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).
%H A198242 Paul D. Hanna, <a href="/A198242/b198242.txt">Table of n, a(n) for n = 0..1000</a>
%F A198242 G.f.: Sum_{n>=0} x^(2*n) * (-x)^(n*(2*n-1)) / Product_{k=1..2*n} (1-(-x)^k)/(1+x).
%e A198242 G.f.: 1 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8 - x^9 + 2*x^11 + 3*x^12 +...
%o A198242 (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)}
%o A198242 for(n=0,81,print1(a(n),", "))
%Y A198242 Cf. A152398 (e_q), A198197 (E_q), A198243 (q-Sinh), A198201 (q-cosh), A198202 (q-sinh).
%Y A198242 Cf. A198199, A198200.
%K A198242 sign
%O A198242 0,12
%A A198242 _Paul D. Hanna_, Aug 07 2012