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 A213627 Expansion of psi(x)^4 / psi(x^3) in powers of x where psi() is a Ramanujan theta function. 3
 1, 4, 6, 7, 9, 6, 7, 15, 12, 12, 13, 6, 12, 18, 18, 13, 15, 18, 12, 24, 12, 13, 27, 12, 24, 15, 12, 24, 28, 30, 12, 27, 18, 12, 30, 18, 19, 27, 24, 24, 27, 24, 36, 30, 18, 19, 24, 24, 24, 45, 18, 12, 45, 30, 24, 28, 18, 36, 36, 36, 24, 15, 36, 36, 51, 18, 25 (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 Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 2501 terms from G. C. Greubel) Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of q^(-1/8) * eta(q^2)^8 * eta(q^3) / (eta(q)^4 * eta(q^6)^2) in powers of q. a(3*n + 2) = 6 * A212907(n). Euler transform of period 6 sequence [4, -4, 3, -4, 4, -3, ...]. - Georg Fischer, Aug 18 2020 EXAMPLE G.f. = 1 + 4*x + 6*x^2 + 7*x^3 + 9*x^4 + 6*x^5 + 7*x^6 + 15*x^7 + 12*x^8 + ... G.f. = q + 4*q^9 + 6*q^17 + 7*q^25 + 9*q^33 + 6*q^41 + 7*q^49 + 15*q^57 + 12*q^65 + ... MAPLE a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*       add([-3, 4, -4, 3, -4, 4][1+irem(d, 6)]*d,         d=numtheory[divisors](j)), j=1..n)/n)     end: seq(a(n), n=0..100);  # Alois P. Heinz, Aug 18 2020 MATHEMATICA a[ n_] := SeriesCoefficient[ 1/8 EllipticTheta[ 2, 0, q]^4 / EllipticTheta[ 2, 0, q^3], {q, 0, 2 n + 1/4}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^8 * eta(x^3 + A) / (eta(x + A)^4 * eta(x^6 + A)^2), n))}; CROSSREFS Cf. A212907. Sequence in context: A078744 A024555 A269330 * A225871 A288383 A001690 Adjacent sequences:  A213624 A213625 A213626 * A213628 A213629 A213630 KEYWORD nonn AUTHOR Michael Somos, Jun 16 2012 STATUS approved

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Last modified September 17 19:01 EDT 2021. Contains 347489 sequences. (Running on oeis4.)