OFFSET
0,2
COMMENTS
It seems that a( (p - 1)/2 ) = 0 if and only if p is in A167860.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
FORMULA
a(n) = b(2*n + 1) where b() is multiplicative with b(2^e) = 0^e, b(3^e) = -2 * (-1)^e if e>0, b(p^e) = b(p) * b(p^(e-1)) - p * b(p^(e-2)) if p>3.
G.f. is a period 1 Fourier series which satisfies f(-1 / (72 t)) = 72 (t/i)^2 f(t) where q = exp(2 Pi i t).
Convolution square is A261278.
EXAMPLE
G.f. = 1 + 2*x - 2*x^2 - 2*x^4 + 4*x^5 - 2*x^6 - 4*x^7 + 2*x^8 - 4*x^9 - 8*x^11 + ...
G.f. = q + 2*q^3 - 2*q^5 - 2*q^9 + 4*q^11 - 2*q^13 - 4*q^15 + 2*q^17 - 4*q^19 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ Sqrt[ QPochhammer[ x^3]^8 + 4 x QPochhammer[ x^6]^8], {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( sqrt( eta(x^3 + A)^8 + 4 * x * eta(x^6 + A)^8 ), n))};
(Magma) A := Basis( CuspForms( Gamma0(72), 2), 142); A[1] + 2*A[3] - 2*A[4];
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Aug 14 2015
STATUS
approved