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

0,2

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