login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
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
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
Sequence in context: A250280 A159982 A195592 * A357788 A022327 A318022
KEYWORD
nonn
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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