The OEIS is supported by the many generous donors to the OEIS 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 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A193557 Expansion of (1/q) * chi(-q) * chi(-q^3) * chi(-q^6)^4 / chi(q)^4 in powers of q where chi() is a Ramanujan theta function. 1
 1, -5, 14, -36, 85, -180, 360, -684, 1246, -2196, 3754, -6264, 10226, -16380, 25804, -40032, 61275, -92628, 138452, -204804, 300040, -435672, 627356, -896400, 1271525, -1791324, 2507426, -3488472, 4825531, -6638688, 9085888, -12373992 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,2 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). LINKS G. C. Greubel, Table of n, a(n) for n = -1..1000 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of - (b(q^2) * c(q^2))^3 / (b(-q)^2 * c(-q) * b(q^4) * c(q^4)^2) in powers of q where b(), c() are cubic AGM functions. Expansion of eta(q)^5 * eta(q^3) * eta(q^4)^4 * eta(q^6)^3 / (eta(q^2)^9 * eta(q^12)^4) in powers of q. Euler transform of period 12 sequence [ -5, 4, -6, 0, -5, 0, -5, 0, -6, 4, -5, 0, ...]. G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (1+u)^2 * v^4 - u^4 * v^2 * (1+v) - 4*u^2 * (1+u) * (1+v) *(4+v) * (4+3*v). a(n) = -(-1)^n * A187198(n). a(n) = A193522(n) unless n=0. a(2*n) = -4 * A128643(n) unless n=0. a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/3)) / (2 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2017 EXAMPLE 1/q - 5 + 14*q - 36*q^2 + 85*q^3 - 180*q^4 + 360*q^5 - 684*q^6 + 1246*q^7 + ... MATHEMATICA eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_] := SeriesCoefficient[eta[q]^5* eta[q^3]*eta[q^4]^4*eta[q^6]^3/(eta[q^2]^9*eta[q^12]^4), {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, Apr 03 2018 *) PROG (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x + A)^5 * eta(x^3 + A) * eta(x^4 + A)^4 * eta(x^6 + A)^3 / (eta(x^2 + A)^9 * eta(x^12 + A)^4), n))} CROSSREFS Cf. A128643, A187198, A193522. Sequence in context: A211562 A261055 A320853 * A187198 A097507 A052951 Adjacent sequences: A193554 A193555 A193556 * A193558 A193559 A193560 KEYWORD sign AUTHOR Michael Somos, Jul 30 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 28 00:05 EST 2022. Contains 358406 sequences. (Running on oeis4.)