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 A123647 Expansion of (eta(q^4) * eta(q^12) / (eta(q) * eta(q^3)))^2 in powers of q. 4
 1, 2, 5, 12, 22, 42, 80, 136, 233, 396, 636, 1020, 1622, 2496, 3822, 5808, 8642, 12786, 18788, 27208, 39184, 56088, 79432, 111912, 156823, 217964, 301517, 415104, 567758, 773244, 1048616, 1414432, 1900524, 2543940, 3389792, 4501164, 5956430 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 FORMULA Euler transform of period 12 sequence [ 2, 2, 4, 0, 2, 4, 2, 0, 4, 2, 2, 0, ...]. G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^2 - v * (1 + 4*u) * (1 + 4*v). G.f. is a period 1 Fourier series which satisfies f(-1 / (12 t)) = (1/16) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A187196. - Michael Somos, Sep 02 2015 Convolution inverse of A187196. - Michael Somos, Sep 02 2015 a(n) ~ exp(2*Pi*sqrt(n/3)) / (32 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Nov 08 2015 EXAMPLE G.f. = x + 2*x^2 + 5*x^3 + 12*x^4 + 22*x^5 + 42*x^6 + 80*x^7 + 136*x^8 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ q (QPochhammer[ q^4] QPochhammer[ q^12] / (QPochhammer[ q^] QPochhammer[ q^3]))^2, {q, 0, n}]; (* Michael Somos, Sep 02 2015 *) PROG (PARI) {a(n) = my(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( (eta(x^4 + A) * eta(x^12 + A) / (eta(x + A) * eta(x^3 + A)))^2, n))}; CROSSREFS Cf. A187196. Sequence in context: A026035 A215183 A086734 * A166249 A326762 A116711 Adjacent sequences: A123644 A123645 A123646 * A123648 A123649 A123650 KEYWORD nonn AUTHOR Michael Somos, Oct 04 2006 STATUS approved

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Last modified September 16 22:04 EDT 2024. Contains 375979 sequences. (Running on oeis4.)