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 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 * A357788 A022327 A318022 Adjacent sequences: A097240 A097241 A097242 * A097244 A097245 A097246 KEYWORD nonn AUTHOR Michael Somos, Aug 02 2004 STATUS approved

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Last modified March 2 07:05 EST 2024. Contains 370460 sequences. (Running on oeis4.)