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 A261154 Expansion of psi(q^6) * f(-q^12) / (psi(-q) * psi(q^9)) in powers of q where psi(), f() are Ramanujan theta functions. 6
 1, 1, 1, 2, 3, 4, 6, 8, 11, 14, 18, 24, 30, 38, 48, 60, 75, 92, 114, 140, 170, 208, 252, 304, 366, 439, 526, 626, 744, 884, 1044, 1232, 1451, 1704, 1998, 2336, 2730, 3182, 3700, 4300, 4986, 5772, 6672, 7700, 8876, 10212, 11736, 13472, 15438, 17673, 20207 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..2000 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of eta(q^2) * eta(q^9) * eta(q^12)^3 / (eta(q) * eta(q^4) * eta(q^6) * eta(q^18)^2) in powers of q. Euler transform of period 36 sequence [1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, -1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, -1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, ...]. G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = 1/2 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A186115. a(n) = A233693(n) unless n=0. a(2*n) = A212484(n). a(n) ~ exp(2*Pi*sqrt(n)/3) / (4*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Nov 16 2017 EXAMPLE G.f. = 1 + x + x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 6*x^6 + 8*x^7 + 11*x^8 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ 2^(1/2) q^(1/2) EllipticTheta[ 2, 0, q^3] QPochhammer[ q^12] / (EllipticTheta[ 2, Pi/4, q^(1/2)] EllipticTheta[ 2, 0, q^(9/2)]), {q, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^9 + A) * eta(x^12 + A)^3 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^18 + A)^2), n))}; CROSSREFS Cf. A186115, A212484, A233693. Sequence in context: A279075 A062464 A053270 * A233693 A003412 A038348 Adjacent sequences:  A261151 A261152 A261153 * A261155 A261156 A261157 KEYWORD nonn AUTHOR Michael Somos, Aug 10 2015 STATUS approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)