|
| |
|
|
A002284
|
|
q-expansion of modular form of weight 13/2: eta(8 tau)^12 * theta(tau).
|
|
1
|
|
|
|
0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, -12, -22, 0, 0, -24, 0, 0, 0, 56, 84, 0, 0, 108, 0, 0, 0, -112, -66, 0, 0, -176, 0, 0, 0, 9, -398, 0, 0, -196, 0, 0, 0, 364, 990, 0, 0, 1056, 0, 0, 0, -616, 70, 0, 0, -728, 0, 0, 0, 432, -2354, 0, 0, -1472, 0, 0, 0, -240, 1080, 0, 0, 990, 0, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,6
|
|
|
LINKS
|
|
|
|
FORMULA
|
Expansion of eta(q^2)^5 * eta(q^8)^12 / (eta(q) * eta(q^4))^2 in powers of q.
Euler transform of period 8 sequence [ 2, -3, 2, -1, 2, -3, 2, -13, ...]. - Michael Somos, Mar 06 2004
G.f.: x^4 * (Product_{k>0} (1 - x^(2*k))^5 * (1 - x^(8*k))^12 / ((1 - x^k) * (1 - x^(4*k)))^2). - Michael Somos, Mar 06 2004
|
|
|
EXAMPLE
|
G.f. = q^4 + 2*q^5 + 2*q^9 - 12*q^13 - 22*q^14 - 24*q^17 + 56*q^21 + ...
|
|
|
MATHEMATICA
|
max = 76; f[x_] := x^4*Product[ (1 - x^(2k))^5 (1 - x^(8k))^12/((1 - x^k) (1 - x^(4k)))^2, {k, 1, max}]; CoefficientList[ Series[ f[x], {x, 0, max}], x] (* Jean-François Alcover, Dec 12 2011, after Michael Somos *)
QP = QPochhammer; s = q^4*QP[q^2]^5*(QP[q^8]^12/(QP[q]*QP[q^4])^2) + O[q]^80; CoefficientList[s, q] (* Jean-François Alcover, Nov 24 2015 *)
|
|
|
PROG
|
(PARI) {a(n) = if( n<4, 0, n-=4; polcoeff( eta(x^8 + x * O(x^n))^12 * sum(k=1, sqrtint(n), 2*x^k^2, 1), n))}; /* Michael Somos, Mar 06 2004 */
(PARI) {a(n) = local(A); if( n<4, 0, n-=4; A = x * O(x^n); polcoeff(eta(x^2 + A)^5 * eta(x^8 + A)^12 / (eta(x + A)^2 * eta(x^4 + A)^2), n))}; /* Michael Somos, Mar 06 2004 */
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
sign,nice
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
