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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

T. D. Noe, Table of n, a(n) for n=0..1004

R. E. Borcherds, A Siegel cusp form of weight 12 ...

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

Sequence in context: A130209 A109127 A263456 * A016424 A108913 A237885

Adjacent sequences:  A002281 A002282 A002283 * A002285 A002286 A002287

KEYWORD

sign,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 31 22:45 EDT 2020. Contains 334756 sequences. (Running on oeis4.)