The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A227213 Expansion of (eta(q^5) * eta(q^10) / (eta(q) * eta(q^2)))^2 in powers of q. 2
 1, 2, 7, 14, 35, 64, 136, 238, 457, 770, 1377, 2248, 3822, 6072, 9920, 15406, 24386, 37114, 57240, 85590, 129152, 190104, 281542, 408616, 595425, 853244, 1225705, 1736304, 2462830, 3452240, 4841442, 6721262, 9329664, 12837572, 17653935, 24092998, 32850206 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number 9 of the 14 eta-quotients listed in Table 2 of Moy 2013. LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 Richard Moy, Congruences among power series coefficients of modular forms, arXiv:1309.4320 [math.NT], 2013. FORMULA Euler transform of period 10 sequence [ 2, 4, 2, 4, 0, 4, 2, 4, 2, 0, ...]. G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = 1/25 * g(t) where q = exp(2 Pi i t) and g() is the g.f. for A132041. G.f.: x * (Product_{k>0} ( (1 - x^(5*k)) * (1 - x^(10*k))) / ((1 - x^k) * (1 - x^(2*k))))^2. [corrected by Vaclav Kotesovec, Sep 08 2015] Convolution inverse of A132041. a(n) ~ exp(2*Pi*sqrt(2*n/5)) / (2^(3/4) * 5^(9/4) * n^(3/4)). - Vaclav Kotesovec, Sep 08 2015 EXAMPLE G.f. = q + 2*q^2 + 7*q^3 + 14*q^4 + 35*q^5 + 64*q^6 + 136*q^7 + 238*q^8 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ q (QPochhammer[ q^5] QPochhammer[ q^10] / (QPochhammer[ q] QPochhammer[ q^2]))^2, {q, 0, n}]; (* Michael Somos, Jan 10 2015 *) nmax = 40; Rest[CoefficientList[Series[x * Product[((1 - x^(5*k)) * (1 - x^(10*k)) / ((1 - x^k) * (1 - x^(2*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Sep 08 2015 *) PROG (PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( (eta(x^5 + A) * eta(x^10 + A) / (eta(x + A) * eta(x^2 + A)))^2, n))}; CROSSREFS Cf. A132041. Sequence in context: A290682 A000147 A128902 * A319455 A060552 A274868 Adjacent sequences:  A227210 A227211 A227212 * A227214 A227215 A227216 KEYWORD nonn AUTHOR Michael Somos, Sep 19 2013 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 22 16:37 EST 2020. Contains 331152 sequences. (Running on oeis4.)