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 A164612 Expansion of q^(-1) * phi^2(q) * chi^3(q^9) / (chi(q^3) * phi^2(q^9)) in powers of q where phi(), chi() are Ramanujan theta functions. 4
 1, 4, 4, -1, 0, 4, 1, 0, 0, 1, 0, -8, -1, 0, -8, 0, 0, 4, 1, 0, 16, -2, 0, 16, 0, 0, -4, 2, 0, -32, -3, 0, -32, 1, 0, 8, 4, 0, 56, -4, 0, 56, 1, 0, -16, 4, 0, -96, -6, 0, -92, 1, 0, 24, 5, 0, 160, -8, 0, 152, 1, 0, -40, 8, 0, -252, -10, 0, -240, 2, 0, 64, 11, 0, 392, -14, 0, 368, 4, 0, -96, 14, 0, -600, -19, 0, -560, 4, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,2 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 = -1..1000 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of chi(q^3)^3 / (q * chi(q)) + 4 + 4 * q * chi(q) / chi(q^3)^3 in powers of q where chi() is a Ramanujan theta function. Expansion of eta(q^2)^10 * eta(q^3) * eta(q^9) * eta(q^12) * eta(q^36) / (eta(q)^4 * eta(q^4)^4 * eta(q^6)^2 * eta(q^18)^4) in powers of q. Euler transform of period 36 sequence [ 4, -6, 3, -2, 4, -5, 4, -2, 2, -6, 4, -2, 4, -6, 3, -2, 4, -2, 4, -2, 3, -6, 4, -2, 4, -6, 2, -2, 4, -5, 4, -2, 3, -6, 4, 0, ...]. a(3*n) = 0 unless n=0. a(n) = A164268(n) unless n=0. Convolution of A164613 and A062244. EXAMPLE G.f. = 1/q + 4 + 4*q - q^2 + 4*q^4 + q^5 + q^8 - 8*q^10 - q^11 - 8*q^13 + ... MATHEMATICA eta[x_] := QPochhammer[x]; A164612[n_] := SeriesCoefficient[eta[q^2]^10* eta[q^3]*eta[q^9]*eta[q^12]*eta[q^36]/(eta[q]^4*eta[q^4]^4*eta[q^6]^2 *eta[q^18]^4), {q, 0, n}]; Table[A164612[n], {n, 0, 50}] (* G. C. Greubel, Aug 10 2017 *) PROG (PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x^2 + A)^10 * eta(x^3 + A) * eta(x^9 + A) * eta(x^12 + A) * eta(x^36 + A) / (eta(x + A)^4 * eta(x^4 + A)^4 * eta(x^6 + A)^2 * eta(x^18 + A)^4), n))}; CROSSREFS Cf. A062244, A164268, A164613. Sequence in context: A070430 A336302 A163353 * A309748 A180401 A057270 Adjacent sequences:  A164609 A164610 A164611 * A164613 A164614 A164615 KEYWORD sign AUTHOR Michael Somos, Aug 17 2009 STATUS approved

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)