cp's OEIS Frontend

A198243 G.f.: q-Sinh(x) evaluated at q=-x.

%I A198243 #6 Oct 20 2024 19:25:40
%S A198243 1,0,0,0,0,-1,-2,-2,-1,0,0,-1,-2,-2,0,4,7,6,3,2,3,4,5,6,6,6,8,10,6,-6,
%T A198243 -18,-20,-13,-7,-8,-13,-16,-15,-13,-15,-25,-41,-53,-53,-44,-32,-16,5,
%U A198243 22,25,18,13,14,19,29,41,44,38,43,72,109,130,135,146,180,232,274
%N A198243 G.f.: q-Sinh(x) evaluated at q=-x.
%C A198243 Note: q-Sinh(x) = Sum_{n>=0} x^(2*n+1) * q^(n*(2*n+1)) / Product_{k=1..2*n+1} (1-q^k)/(1-q).
%F A198243 G.f.: Sum_{n>=0} x^(2*n+1) * (-x)^(n*(2*n+1)) / Product_{k=1..2*n+1} (1-(-x)^k)/(1+x).
%e A198243 G.f.: x - x^6 - 2*x^7 - 2*x^8 - x^9 - x^12 - 2*x^13 - 2*x^14 + 4*x^16 + 7*x^17 +...
%o A198243 (PARI) {a(n)=local(Sinh_q=sum(k=0, sqrtint(n+4), (-x)^(k*(2*k+1))*x^(2*k+1)/(prod(j=1, 2*k+1, (1-(-x)^j)/(1+x))+x*O(x^n)))); polcoeff(Sinh_q, n)}
%o A198243 for(n=0,81,print1(a(n),", "))
%Y A198243 Cf. A152398 (e_q), A198197 (E_q), A198242 (q-Cosh), A198201 (q-cosh), A198202 (q-sinh).
%Y A198243 Cf. A198199, A198200.
%K A198243 sign
%O A198243 1,7
%A A198243 _Paul D. Hanna_, Aug 07 2012