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

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A320068 Expansion of Product_{k>0} 1/theta_3(q^k), where theta_3() is the Jacobi theta function. 11
 1, -2, 2, -6, 12, -18, 30, -50, 84, -132, 198, -306, 476, -706, 1026, -1522, 2234, -3202, 4564, -6506, 9224, -12934, 17982, -24982, 34612, -47496, 64798, -88340, 119944, -161814, 217462, -291562, 389642, -518442, 687222, -908934, 1199040, -1575730, 2064466, -2699378, 3520540 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Seiichi Manyama) Eric Weisstein's World of Mathematics, Jacobi Theta Functions FORMULA Convolution inverse of A320067. Expansion of Product_{k>0} (eta(q^k)*eta(q^(4*k)))^2 / eta(q^(2*k))^5. Expansion of Product_{k>0} theta_4(q^(2*k-1))/theta_4(q^(2*k)), where theta_4() is the Jacobi theta function. - Seiichi Manyama, Oct 26 2018 MATHEMATICA nmax = 50; CoefficientList[Series[1/Product[EllipticTheta[3, 0, x^k], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 05 2018 *) nmax = 50; CoefficientList[Series[Product[(1 + x^(2*k*j))^2/((1 - x^(k*j))*(1 + x^(k*j))^3), {k, 1, nmax}, {j, 1, Floor[nmax/k] + 1}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 08 2018 *) PROG (PARI) m=50; x='x+O('x^m); Vec(prod(k=1, 2*m, prod(j=1, floor(2*m/k)+1, (1 + x^(2*k*j))^2/((1 - x^(k*j))*(1 + x^(k*j))^3) ))) \\ G. C. Greubel, Oct 29 2018 (MAGMA) m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[(&*[(1 + x^(2*k*j))^2/((1 - x^(k*j))*(1 + x^(k*j))^3): j in [1..(Floor(2*m/k)+1)]]): k in [1..2*m]]))); // G. C. Greubel, Oct 29 2018 CROSSREFS Cf. A000122, A004402, A320067, A320069, A320070, A320968, A320992. Sequence in context: A290518 A242882 A157285 * A345988 A275439 A173392 Adjacent sequences:  A320065 A320066 A320067 * A320069 A320070 A320071 KEYWORD sign AUTHOR Seiichi Manyama, Oct 05 2018 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.

Last modified December 7 22:50 EST 2021. Contains 349590 sequences. (Running on oeis4.)