login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A198243 G.f.: q-Sinh(x) evaluated at q=-x. 5
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, -18, -20, -13, -7, -8, -13, -16, -15, -13, -15, -25, -41, -53, -53, -44, -32, -16, 5, 22, 25, 18, 13, 14, 19, 29, 41, 44, 38, 43, 72, 109, 130, 135, 146, 180, 232, 274 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

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).

LINKS

Table of n, a(n) for n=1..67.

FORMULA

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).

EXAMPLE

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 +...

PROG

(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)}

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

CROSSREFS

Cf. A152398 (e_q), A198197 (E_q), A198242 (q-Cosh), A198201 (q-cosh), A198202 (q-sinh).

Cf. A198199, A198200.

Sequence in context: A276204 A024712 A281497 * A164965 A021823 A131026

Adjacent sequences:  A198240 A198241 A198242 * A198244 A198245 A198246

KEYWORD

sign

AUTHOR

Paul D. Hanna, Aug 07 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 20 14:17 EST 2021. Contains 340302 sequences. (Running on oeis4.)