A263348 - OEIS

%I #9 Aug 01 2018 00:48:51

%S 1,2,5,10,20,36,63,106,175,280,439,676,1024,1528,2250,3276,4718,6728,

%T 9507,13324,18526,25574,35064,47774,64701,87134,116722,155572,206362,

%U 272492,358265,469096,611801,794916,1029126,1327738,1707322,2188432,2796528,3563048

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

%H G. C. Greubel, <a href="/A263348/b263348.txt">Table of n, a(n) for n = 0..2500</a>

%F 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, ...].

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

%F Convolution square of A094023.

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

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

%o (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))};

%o (PARI) q='q+O('q^99); Vec((eta(q^6)*eta(q^10)/(eta(q)*eta(q^15)))^2) \\ _Altug Alkan_, Jul 31 2018

%Y Cf. A094023, A145728.

%K nonn

%O 0,2

%A _Michael Somos_, Oct 15 2015