A260165 Expansion of f(x, x^2) * f(x, x^3)^3 in powers of x where f(, ) is Ramanujan's general theta function.
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
Offset: 0
Keywords
Examples
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 + ...
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
Crossrefs
Cf. A260158.
Programs
-
Mathematica
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^3] QPochhammer[ x^2]^5 / EllipticTheta[ 4, 0, x]^2, {x, 0, n}]; -
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))};
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).
Comments