|
Search: id:A085261
|
|
|
| A085261 |
|
Expansion of q^(1/24)eta(q^2)^4eta(q^8)^2/(eta(q)eta(q^4)^6) in powers of q. |
|
+0
1
|
|
| 1, 1, -2, -1, 5, 3, -9, -5, 18, 10, -30, -16, 53, 29, -85, -44, 139, 73, -215, -110, 335, 172, -502, -253, 755, 382, -1104, -550, 1614, 805, -2312, -1142, 3305, 1631, -4650, -2277, 6525, 3193, -9041, -4395, 12486, 6063, -17070, -8247, 23255, 11218, -31414, -15090, 42289, 20285
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Euler transform of period 8 sequence [1,-3,1,3,1,-3,1,1,...].
|
|
REFERENCES
|
R. P. Stanley, Problem 10969, Amer. Math. Monthly, 109 (Oct 2002), p. 760.
|
|
LINKS
|
G. E. Andrews, On a Partition Function of Richard Stanley
|
|
FORMULA
|
G.f.: Product_{k>0} (1+x^(2k-1))/((1-x^(4k))(1+x^(4k-2))^2).
|
|
PROGRAM
|
(PARI) a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff(eta(x^2+A)^4*eta(x^8+A)^2/eta(x+A)/eta(x^4+A)^6, n))
(PARI) a(n)=polcoeff(prod(k=1, (n+1)\2, 1+x^(2*k-1), 1+x*O(x^n))/prod(k=1, (n+2)\4, (1-x^(4*k))*(1+x^(4*k-2))^2, 1+x*O(x^n)), n)
|
|
CROSSREFS
|
Sequence in context: A058683 A026205 A082748 this_sequence A131119 A114901 A113178
Adjacent sequences: A085258 A085259 A085260 this_sequence A085262 A085263 A085264
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Jun 23 2003
|
|
|
Search completed in 0.002 seconds
|
