A257632 Expansion of eta(q^6)^3 * eta(q^10)^3 / (eta(q^2) * eta(q^3)^2 * eta(q^5)^2 * eta(q^30)) in powers of q.

1, 0, 1, 2, 2, 4, 5, 6, 11, 14, 17, 24, 32, 40, 54, 70, 84, 112, 143, 172, 222, 274, 332, 422, 515, 620, 766, 932, 1118, 1364, 1645, 1952, 2365, 2832, 3346, 4014, 4760, 5608, 6680, 7876, 9235, 10904, 12802, 14954, 17552, 20506, 23830, 27842, 32390, 37504

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

Euler transform of period 30 sequence [ 0, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 2, 1, 0, 0, 2, 1, 2, 1, 0, 0, ...].

a(n) = A132968(2*n).

Example

G.f. = 1 + x^2 + 2*x^3 + 2*x^4 + 4*x^5 + 5*x^6 + 6*x^7 + 11*x^8 + 14*x^9 + 17*x^10 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ q^6]^3 QPochhammer[ q^10]^3 / (QPochhammer[ q^2] QPochhammer[ q^3]^2 QPochhammer[ q^5]^2 QPochhammer[ q^30]), {q, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^6 + A)^3 * eta(x^10 + A)^3 / (eta(x^2 + A) * eta(x^3 + A)^2 * eta(x^5 + A)^2 * eta(x^30 + A)), n))};

Crossrefs

Cf. A132967, A132968.

Sequence in context: A232166 A325555 A138883 * A325554 A367962 A107849

Adjacent sequences: A257629 A257630 A257631 * A257633 A257634 A257635

Keyword

nonn

Author

Michael Somos, Nov 04 2015

Status

approved