login
A263348
Expansion of (eta(q^6) * eta(q^10) / (eta(q) * eta(q^15)))^2 in powers of q.
1
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
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
Sequence in context: A160461 A365631 A117487 * A328548 A294536 A325650
KEYWORD
nonn
AUTHOR
Michael Somos, Oct 15 2015
STATUS
approved