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 A260165 Expansion of f(x, x^2) * f(x, x^3)^3 in powers of x where f(, ) is Ramanujan's general theta function. 2
 1, 4, 7, 10, 13, 14, 18, 22, 25, 28, 26, 34, 37, 36, 43, 38, 49, 54, 56, 58, 43, 64, 67, 70, 73, 62, 79, 72, 90, 88, 74, 98, 97, 100, 90, 84, 108, 112, 115, 126, 98, 108, 127, 130, 140, 110, 139, 142, 126, 148, 133, 154, 152, 160, 163, 108, 169, 182, 175, 180 (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 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of phi(-x^3) * f(-x^2)^5 / phi(-x)^2 in powers of x where phi(), f() are Ramanujan theta functions. Expansion of q^(-5/12) * eta(q^2)^7 * eta(q^3)^2 / (eta(q)^4 * eta(q^6)) in powers of q. Euler transform of period 6 sequence [4, -3, 2, -3, 4, -4, ...]. a(n) = A260158(2*n). EXAMPLE G.f. = 1 + 4*x + 7*x^2 + 10*x^3 + 13*x^4 + 14*x^5 + 18*x^6 + 22*x^7 + 25*x^8 + ... G.f. = q^5 + 4*q^17 + 7*q^29 + 10*q^41 + 13*q^53 + 14*q^65 + 18*q^77 + 22*q^89 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^3] QPochhammer[ x^2]^5 / EllipticTheta[ 4, 0, x]^2, {x, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^7 * eta(x^3 + A)^2 / (eta(x + A)^4 * eta(x^6 + A)), n))}; CROSSREFS Cf. A260158. Sequence in context: A331207 A090384 A327422 * A055054 A196415 A186327 Adjacent sequences: A260162 A260163 A260164 * A260166 A260167 A260168 KEYWORD nonn AUTHOR Michael Somos, Nov 09 2015 STATUS approved

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Last modified September 10 20:23 EDT 2024. Contains 375794 sequences. (Running on oeis4.)