OFFSET
1,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
a(n) is multiplicative with a(11^e) = 1, a(p^e) = a(p) * a(p^(e-1)) - p * a(p^(e-2)) for p != 11.
a(2*n + 1) = A006571(2*n + 1).
EXAMPLE
G.f. = q + 2*q^2 - q^3 + 2*q^4 + q^5 - 2*q^6 - 2*q^7 - 8*q^8 - 2*q^9 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ q (QPochhammer[ q] QPochhammer[ q^11])^2 + 4 q^2 (QPochhammer[ q^2] QPochhammer[ q^22])^2 + 8 q^4 (QPochhammer[ q^4] QPochhammer[ q^44])^2, {q, 0, n}];
PROG
(PARI) {a(n) = my(A, F); if( n<1, 0, A = x * O(x^n); F = x * (eta(x + A) * eta(x^11 + A))^2; polcoeff( F + 4*subst(F, x, x^2) + 8*subst(F, x, x^4), n))};
(Magma) A := Basis( CuspForms( Gamma0(44), 2), 79); A[1] + 2*A[2] - A[3] + 2*A[4];
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Michael Somos, Dec 10 2016
STATUS
approved