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 A182056 Expansion of psi(x) * chi(-x^3) * f(-x^16) * chi(-x^24) / phi(-x^12)^2 in powers of x where phi(), psi(), chi(), f() are Ramanujan theta functions. 3
 1, 1, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 4, 4, 0, 0, -6, -1, 0, 0, 1, -8, 0, 0, 11, 14, 0, 0, -19, -4, 0, 0, 4, -23, 0, 0, 31, 40, 0, 0, -50, -10, 0, 0, 11, -60, 0, 0, 77, 98, 0, 0, -122, -24, 0, 0, 28, -140, 0, 0, 173, 224, 0, 0, -273, -54, 0, 0, 62, -304, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 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..1000 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of q^(-1/3) * eta(q^2)^2 * eta(q^3) * eta(q^16) * eta(q^24)^3 / (eta(q) * eta(q^6) * eta(q^12)^4 * eta(q^48)) in powers of q. Euler transform of period 48 sequence [ 1, -1, 0, -1, 1, -1, 1, -1, 0, -1, 1, 3, 1, -1, 0, -2, 1, -1, 1, -1, 0, -1, 1, 0, 1, -1, 0, -1, 1, -1, 1, -2, 0, -1, 1, 3, 1, -1, 0, -1, 1, -1, 1, -1, 0, -1, 1, 0, ...]. a(4*n + 2) = a(4*n + 3) = 0. a(4*n) = A182032(12*n - 1). a(4*n + 1) = A182032(12*n + 2). EXAMPLE 1 + x - x^4 - 2*x^9 + 4*x^12 + 4*x^13 - 6*x^16 - x^17 + x^20 + ... 1/q + q^2 - q^11 - 2*q^26 + 4*q^35 + 4*q^38 - 6*q^47 - q^50 + q^59 + ... MATHEMATICA QP := QPochhammer; A182056[n_] := SeriesCoefficient[QP[q^2]^2*QP[q^3]* QP[q^16]*QP[q^24]^3/(QP[q]* QP[q^6]*QP[q^12]^4*QP[q^48]), {q, 0, n}]; Table[A182056[n], {n, 0, 50}] (* G. C. Greubel, Dec 24 2017 *) PROG (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A) * eta(x^16 + A) * eta(x^24 + A)^3 / (eta(x + A) * eta(x^6 + A) * eta(x^12 + A)^4 * eta(x^48 + A)), n))} CROSSREFS Cf. A182032. Sequence in context: A072071 A329264 A045836 * A072070 A137830 A137828 Adjacent sequences:  A182053 A182054 A182055 * A182057 A182058 A182059 KEYWORD sign AUTHOR Michael Somos, Apr 08 2012 STATUS approved

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)