This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A097243 Expansion of 1 + 32 * (eta(q^4) / eta(q))^8 in powers of q. 4
 1, 32, 256, 1408, 6144, 22976, 76800, 235264, 671744, 1809568, 4640256, 11404416, 27009024, 61905088, 137803776, 298806528, 632684544, 1310891584, 2662655232, 5310231424, 10412576768, 20098970624, 38231811072, 71734039808, 132875747328, 243175399136 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Expansion of a q-series used in construction of j(tau) to j(2tau) iteration. REFERENCES H. Cohn, Introduction to the construction of class fields, Cambridge 1985, p. 191 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (u+3)^2 - 8*(u+1)*v^2. a(n) = 32*A092877(n), if n>0. a(n) = A007096(4*n). a(n) = A014969(2*n) = A139820(2*n) = A189925(4*n) = A212318(4*n) = A232358(4*n). - Michael Somos, Dec 15 2016 G.f. is a period 1 Fourier series which satisfies f(-1 / (4 t)) = 1/8 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A007248. - Michael Somos, Dec 15 2016 a(n) ~ exp(2*Pi*sqrt(n))/(16*n^(3/4)). - Vaclav Kotesovec, Sep 08 2017 EXAMPLE G.f. = 1 + 32*x + 256*x^2 + 1408*x^3 + 6144*x^4 + 22976*x^5 + 76800*x^6 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ 1 + 32 x (QPochhammer[ x^4] / QPochhammer[ x])^8, {x, 0, n}]; (* Michael Somos, Dec 15 2016 *) PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x^n * O(x); polcoeff( 1 + 32 * x * (eta(x^4 + A) / eta(x + A))^8, n))}; CROSSREFS Cf. A007248, A007096, A014969, A092877, A139820, A189925, A212318, A232358. Sequence in context: A250280 A159982 A195592 * A022327 A189651 A145711 Adjacent sequences:  A097240 A097241 A097242 * A097244 A097245 A097246 KEYWORD nonn,changed AUTHOR Michael Somos, Aug 02 2004 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.