|
Search: id:A134461
|
|
|
| A134461 |
|
Expansion of (phi(q) * psi(-q))^4 in powers of q where phi(), psi() are Ramanujan theta functions. |
|
+0
1
|
|
| 1, 4, -2, -24, -11, 44, 22, -8, 50, -44, -96, 56, -121, -152, 198, 160, 176, 48, -162, 88, -198, -52, 22, -528, 233, 200, -242, -88, -176, 668, 550, 264, -44, -188, 224, -728, 154, -484, -1056, 656, -311, -236, -100, 792, 714, -528, 640, 88, -478, -484, 1566, 968, 192, 780, -1994, -648, -942
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
Y. Martin, Multiplicative eta-quotients, Trans. Amer. Math. Soc. 348 (1996), no. 12, 4825-4856, see page 4852 Table I.
|
|
LINKS
|
W. Stein, Modular Forms Database.
|
|
FORMULA
|
Expansion of q^(-1/2) * (eta(q^2)^4 / (eta(q) * eta(q^4)))^4 in powers of q.
Euler transform of period 4 sequence [ 4, -12, 4, -8, ...].
a(n) = b(2*n+1) where b(n) is multiplicative and b(2^e) = 0^e, b(p^e) = b(p)*b(p^(e-1)) -p^3*b(p^(e-2)).
G.f. is Fourier series of a weight 4 level 16 modular form. f(-1/ (16 t)) = 256 (t/i)^4 f(t) where q = exp(2 pi i t).
G.f.: (Product_{k>0} (1 + x^k) * (1 - x^(2*k))^2 / (1 + x^(2*k)))^4.
|
|
EXAMPLE
|
q + 4*q^3 - 2*q^5 - 24*q^7 - 11*q^9 + 44*q^11 + 22*q^13 - 8*q^15 + ...
|
|
PROGRAM
|
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( ( eta(x^2 + A)^4 / eta(x + A) / eta(x^4 + A) )^4, n))}
|
|
CROSSREFS
|
(-1)^n * A030211 = a(n).
Sequence in context: A157407 A100400 A030211 this_sequence A058167 A140331 A095896
Adjacent sequences: A134458 A134459 A134460 this_sequence A134462 A134463 A134464
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Oct 26 2007
|
|
|
Search completed in 0.002 seconds
|
