A298107 Expansion of (eta(q^4) * eta(q^5) / (eta(q) * eta(q^20)))^2 in powers of q.

1, 2, 5, 10, 18, 30, 51, 80, 124, 190, 281, 410, 592, 840, 1178, 1640, 2253, 3070, 4154, 5570, 7422, 9830, 12932, 16920, 22028, 28520, 36761, 47180, 60280, 76720, 97278, 122880, 154693, 194110, 242776, 302740, 376424, 466710, 577114, 711800, 875707, 1074790

Offset

-1,2

Links

G. C. Greubel, Table of n, a(n) for n = -1..1500

Formula

Euler transform of period 20 sequence [2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (20 t)) = f(t) where q = exp(2 Pi i t).

G.f.: 1/x * Product_{k>0} ((1 - x^(4*k)) * (1 - x^(5*k)))^2 / ((1 - x^k) * (1 - x^(20*k)))^2.

a(n) = A058555(n) unless n=0. Convolution square of A058664.

a(n) ~ exp(2*Pi*sqrt(n/5)) / (2*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 21 2018

Example

G.f. = q^-1 + 2 + 5*q + 10*q^2 + 18*q^3 + 30*q^4 + 51*q^5 + 80*q^6 + ...

Mathematica

a[ n_] := SeriesCoefficient[ 1/q (QPochhammer[ q^4] QPochhammer[ q^5])^2 / (QPochhammer[ q] QPochhammer[ q^20])^2, {q, 0 , n}];

Prog

(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x^4 + A) * eta(x^5 + A) / (eta(x + A) * eta(x^20 + A)))^2, n))};

Crossrefs

Cf. A058555, A058664.

Sequence in context: A104688 A117485 A084835 * A034350 A006327 A185721

Adjacent sequences: A298104 A298105 A298106 * A298108 A298109 A298110

Keyword

nonn

Author

Michael Somos, Jan 12 2018

Status

approved