A198202 - OEIS

%I #7 Feb 16 2025 10:26:17

%S 1,0,1,2,3,5,8,13,22,31,32,89,115,126,122,118,127,150,178,198,653,747,

%T 835,921,1011,1113,1236,1377,1520,1661,1823,6483,6894,7584,8646,9906,

%U 11074,11995,12787,13752,15105,16742,18316,19608,71188,78144,84610,90794,97895

%N G.f.: q-sinh(x) evaluated at q=-x.

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

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

%e 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 (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 for(n=0,81,print1(a(n),", "))

%Y Cf. A152398 (e_q), A198197 (E_q), A198242 (q-Cosh), A198243 (q-Sinh), A198201 (q-cosh).

%Y Cf. A198199, A198200.

%K nonn

%O 1,4

%A _Paul D. Hanna_, Aug 07 2012