This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A198202 #7 Feb 16 2025 10:26:17
%S A198202 1,0,1,2,3,5,8,13,22,31,32,89,115,126,122,118,127,150,178,198,653,747,
%T A198202 835,921,1011,1113,1236,1377,1520,1661,1823,6483,6894,7584,8646,9906,
%U A198202 11074,11995,12787,13752,15105,16742,18316,19608,71188,78144,84610,90794,97895
%N A198202 G.f.: q-sinh(x) evaluated at q=-x.
%C A198202 Note: q-sinh(x) = Sum_{n>=0} x^(2*n+1) / Product_{k=1..2*n+1} (1-q^k)/(1-q).
%F A198202 G.f.: Sum_{n>=0} x^(2*n+1) / Product_{k=1..2*n+1} (1-(-x)^k)/(1+x).
%e A198202 G.f.: x + x^3 + 2*x^4 + 3*x^5 + 5*x^6 + 8*x^7 + 13*x^8 + 22*x^9 + 31*x^10 +...
%o A198202 (PARI) {a(n)=local(Sinh_q=sum(k=0, sqrtint(n+4), x^(2*k+1)/(prod(j=1, 2*k+1, (1-(-x)^j)/(1+x))+x*O(x^n)))); polcoeff(Sinh_q, n)}
%o A198202 for(n=0,81,print1(a(n),", "))
%Y A198202 Cf. A152398 (e_q), A198197 (E_q), A198242 (q-Cosh), A198243 (q-Sinh), A198201 (q-cosh).
%Y A198202 Cf. A198199, A198200.
%K A198202 nonn
%O A198202 1,4
%A A198202 _Paul D. Hanna_, Aug 07 2012