A229893 Expansion of q^2 * f(-q) * f(-q^4) * f(-q^16) * f(-q^2, -q^14) in powers of q where f() is a Ramanujan theta function.
1, -1, -2, 1, 0, 2, 2, -1, -2, -1, 2, -1, -2, 0, 0, 0, 1, 3, 2, -2, 2, -6, -4, 3, 0, 4, 0, 3, 2, 0, -4, 0, -2, -2, 0, -3, 0, 2, 0, 0, 4, -5, -2, 1, 6, 0, 4, 0, -3, 2, 2, 5, -8, 2, 4, -6, 0, 3, -4, -9, -8, 0, 8, 0, -2, -5, 4, 6, 0, 10, -2, 4, 6, -3, -6, 2, -2
Offset: 2
Keywords
Examples
G.f. = q^2 - q^3 - 2*q^4 + q^5 + 2*q^7 + 2*q^8 - q^9 - 2*q^10 - q^11 + ...
Links
- G. C. Greubel, Table of n, a(n) for n = 2..2500
- Michael Somos, Introduction to Ramanujan theta functions
- Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
Programs
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Magma
Basis( CuspForms( Gamma1(16), 2), 79)[2];
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Mathematica
a[ n_] := SeriesCoefficient[ q^2 QPochhammer[ q^2, q^16] QPochhammer[ q^14, q^16] QPochhammer[ q^16]^2 QPochhammer[ q] QPochhammer[ q^4], {q, 0, n}] -
PARI
{a(n) = local(A, m); if( n<2, 0, n-=2; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^4 + A) * eta(x^16 + A) * sum( k=0, n\2, if( issquare( 16*k + 9, &m), (-1)^k * x^(2*k), 0), A), n))} -
Sage
CuspForms( Gamma1(16), 2, prec=79).1
Comments