A263348 Expansion of (eta(q^6) * eta(q^10) / (eta(q) * eta(q^15)))^2 in powers of q.

1, 2, 5, 10, 20, 36, 63, 106, 175, 280, 439, 676, 1024, 1528, 2250, 3276, 4718, 6728, 9507, 13324, 18526, 25574, 35064, 47774, 64701, 87134, 116722, 155572, 206362, 272492, 358265, 469096, 611801, 794916, 1029126, 1327738, 1707322, 2188432, 2796528, 3563048

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

Formula

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

a(n) = A094023(2*n) = A145728(2*n).

Convolution square of A094023.

Example

G.f. = 1 + 2*x + 5*x^2 + 10*x^3 + 20*x^4 + 36*x^5 + 63*x^6 + 106*x^7 + ...

Mathematica

a[ n_] := SeriesCoefficient[ (QPochhammer[ q^6] QPochhammer[ q^10] / (QPochhammer[ q] QPochhammer[ q^15]))^2, {q, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^6 + A) * eta(x^10 + A) / (eta(x + A) * eta(x^15 + A)))^2, n))};
(PARI) q='q+O('q^99); Vec((eta(q^6)*eta(q^10)/(eta(q)*eta(q^15)))^2) \\ Altug Alkan, Jul 31 2018

Crossrefs

Cf. A094023, A145728.

Sequence in context: A160461 A365631 A117487 * A328548 A294536 A325650

Adjacent sequences: A263345 A263346 A263347 * A263349 A263350 A263351

Keyword

nonn

Author

Michael Somos, Oct 15 2015

Status

approved