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URL: https://oeis.org/A298107

⇱ A298107 - OEIS

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A298107
Expansion of (eta(q^4) * eta(q^5) / (eta(q) * eta(q^20)))^2 in powers of q.
2
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
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
Sequence in context: A104688 A117485 A084835 * A034350 A006327 A185721
KEYWORD
nonn
AUTHOR
Michael Somos, Jan 12 2018
STATUS
approved