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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 * A022327 A189651 A145711

Adjacent sequences:  A097240 A097241 A097242 * A097244 A097245 A097246

KEYWORD

nonn,changed

AUTHOR

Michael Somos, Aug 02 2004

STATUS

approved

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Last modified December 12 15:01 EST 2017. Contains 295939 sequences.