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 A259392 Expansion of phi(-x^5) * f(x^2, x^8) / psi(-x)^2 in powers of x where phi, psi, f(,) are Ramanujan theta functions. 2
 1, 2, 4, 8, 14, 22, 35, 54, 82, 122, 176, 254, 362, 504, 697, 960, 1307, 1762, 2360, 3142, 4158, 5462, 7133, 9280, 12013, 15462, 19818, 25314, 32198, 40782, 51476, 64768, 81226, 101522, 126502, 157216, 194846, 240784, 296802, 365006, 447794, 548042, 669254 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). LINKS G. C. Greubel, Table of n, a(n) for n = 0..2500 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Euler transform of period 20 sequence [ 2, 1, 2, 1, 0, 0, 2, 3, 2, -2, 2, 3, 2, 0, 0, 1, 2, 1, 2, 0, ...]. a(n) = A132225(5*n + 1). a(n) ~ exp(2*Pi*sqrt(n/5)) / (5^(5/4) * n^(3/4)). - Vaclav Kotesovec, Jul 04 2018 EXAMPLE G.f. = 1 + 2*x + 4*x^2 + 8*x^3 + 14*x^4 + 22*x^5 + 35*x^6 + 54*x^7 + ... G.f. = q + 2*q^6 + 4*q^11 + 8*q^16 + 14*q^21 + 22*q^26 + 35*q^31 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ QPochhammer[ -x^2, x^10] QPochhammer[ -x^8, x^10] (QPochhammer[ x^2, x^4] QPochhammer[ x^5] / QPochhammer[ x])^2, {x, 0, n}]; QP := QPochhammer; f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]*QP[x*y, x*y]; A:= f[-x^5, -x^5]*f[x^2, x^8]/f[-x, - x^3]^2; a:= CoefficientList[Series[A, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 04 2018 *) PROG (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^[ 0, -2, -1, -2, -1, 0, 0, -2, -3, -2, 2, -2, -3, -2, 0, 0, -1, -2, -1, -2][k%20 + 1]), n))}; CROSSREFS Cf. A132225. Sequence in context: A053798 A305497 A231429 * A261968 A138526 A286522 Adjacent sequences:  A259389 A259390 A259391 * A259393 A259394 A259395 KEYWORD nonn AUTHOR Michael Somos, Jun 25 2015 STATUS approved

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Last modified August 14 09:14 EDT 2020. Contains 336480 sequences. (Running on oeis4.)