OFFSET
0,3
COMMENTS
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from G. C. Greubel)
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Euler transform of period 7 sequence [ 1, -3, 2, 2, -3, 1, 0, ...].
G.f.: T(q)/(T(q)-1), where T(q) = 1/q + 3 + 4*q + ... (cf. A108481). - Seiichi Manyama, Oct 11 2018
EXAMPLE
G.f. = 1 + q - 2*q^2 + 5*q^4 - 4*q^5 - 7*q^6 + 12*q^7 + 4*q^8 - 22*q^9 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ Product[ (1 - x^k)^{-1, 3, -2, -2, 3, -1, 0}[[Mod[k, 7, 1]]], {k, n}], {x, 0, n}];
(* alternative program *)
QP:= QPochhammer; a[n_]:= SeriesCoefficient[(QP[q^2, q^7]*QP[q^5, q^7])^3/ (QP[q, q^7]*QP[q^6, q^7]*QP[q^3, q^7]^2*QP[q^4, q^7]^2), {q, 0, n}];
Table[a[n], {n, 0, 50}] (* G. C. Greubel, Mar 18 2018 *)
PROG
(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^[0, -1, 3, -2, -2, 3, -1][k%7 + 1]), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Oct 04 2015
STATUS
approved