A198202 G.f.: q-sinh(x) evaluated at q=-x.

1, 0, 1, 2, 3, 5, 8, 13, 22, 31, 32, 89, 115, 126, 122, 118, 127, 150, 178, 198, 653, 747, 835, 921, 1011, 1113, 1236, 1377, 1520, 1661, 1823, 6483, 6894, 7584, 8646, 9906, 11074, 11995, 12787, 13752, 15105, 16742, 18316, 19608, 71188, 78144, 84610, 90794, 97895

Offset

1,4

Comments

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

Links

Table of n, a(n) for n=1..49.

Formula

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

Example

 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 +...

Prog

 (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)}
for(n=0, 81, print1(a(n), ", "))

Crossrefs

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

Cf. A198199, A198200.

Sequence in context: A041247 A117770 A053412 * A349840 A293639 A320356

Adjacent sequences: A198199 A198200 A198201 * A198203 A198204 A198205

Keyword

nonn

Author

Paul D. Hanna, Aug 07 2012

Status

approved