A253183 Expansion of (q^3 * psi(q) * psi(q^23))^2 in powers of q where psi() is a Ramanujan theta function.

1, 2, 1, 2, 2, 0, 3, 2, 0, 2, 2, 2, 1, 2, 0, 2, 4, 0, 2, 0, 1, 4, 2, 2, 6, 4, 4, 6, 2, 8, 5, 4, 4, 4, 6, 2, 8, 2, 6, 10, 0, 4, 3, 4, 8, 6, 5, 6, 7, 4, 6, 8, 7, 4, 8, 6, 5, 8, 3, 10, 6, 8, 8, 0, 4, 8, 9, 6, 6, 12, 8, 8, 11, 8, 10, 8, 9, 4, 14, 12, 10, 12, 8, 8

Offset

6,2

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 = 6..2500

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of (eta(q^2) * eta(q^46))^4 / (eta(q) * eta(q^23))^2 in powers of q.

Euler transform of a period 46 sequence.

G.f.: x^6 * (Sum_{k>0} x^(k * (k-1) / 2))^2 * (Sum_{k>0} x^(23 * k * (k-1) / 2))^2.

G.f.: x^6 * (Product_{k>0} (1 + x^k) * (1 - x^(2*k)) * (1 + x^(23*k)) * (1 - x^(46*k)))^2.

Convolution square of A033782.

Example

G.f. = q^6 + 2*q^7 + q^8 + 2*q^9 + 2*q^10 + 3*q^12 + 2*q^13 + 2*q^15 + ...

Mathematica

a[ n_] := SeriesCoefficient[ q^6 (QPochhammer[ q^2] QPochhammer[ q^46])^4 / (QPochhammer[ q] QPochhammer[ q^23])^2, {q, 0 , n}];

Prog

(PARI) {a(n) = my(A); if( n<6, 0, n -= 6; A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^46 + A))^4 / (eta(x + A) * eta(x^23 + A))^2, n))};

Crossrefs

Cf. A033782.

Sequence in context: A226005 A134343 A008441 * A108804 A284467 A200227

Adjacent sequences: A253180 A253181 A253182 * A253184 A253185 A253186

Keyword

nonn

Author

Michael Somos, Mar 23 2015

Status

approved