# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a232714 Showing 1-1 of 1 %I A232714 #15 Mar 12 2021 22:24:47 %S A232714 1,-1,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,-1,0,0,0,0,0,0,0,0, %T A232714 0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1, %U A232714 0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0 %N A232714 Expansion of f(-x, -x^6) in powers of x where f is Ramanujan's two-variable theta function. %C A232714 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). %H A232714 Seiichi Manyama, Table of n, a(n) for n = 0..10000 %H A232714 Michael Somos, Introduction to Ramanujan theta functions %H A232714 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions %F A232714 Euler transform of period 7 sequence [ -1, 0, 0, 0, 0, -1, -1, ...]. %F A232714 G.f.: Sum_{k in Z} (-1)^k * x^(k * (7*k + 5) / 2). %F A232714 G.f.: Product_{k>0} (1 - x^(7*k-6)) * (1 - x^(7*k-1)) * (1 - x^(7*k)). %F A232714 a(3*n + 2) = a(5*n + 2) = a(5*n + 3) = 0. %F A232714 Convolution inverse of A195849. %F A232714 abs(a(n)) = A274179(n). - _Michael Somos_, Jan 28 2017 %F A232714 a(n) = -(1/n)*Sum_{k=1..n} A284363(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 25 2017 %e A232714 G.f. = 1 - x - x^6 + x^9 + x^19 - x^24 - x^39 + x^46 + x^66 - x^75 - x^100 + ... %e A232714 G.f. = q^25 - q^81 - q^361 + q^529 + q^1089 - q^1369 - q^2209 + q^2601 + q^3721 + ... %t A232714 a[ n_] := SeriesCoefficient[ SeriesCoefficient[ QPochhammer[ q, q^7] QPochhammer[ q^6, q^7] QPochhammer[ q^7], {q, 0, n}]; %o A232714 (PARI) {a(n) = my(m); if( issquare( 56*n + 25, &m), (-1)^round( m / 14), 0)}; %Y A232714 Cf. A195849, A274179. %K A232714 sign %O A232714 0,1 %A A232714 _Michael Somos_, Nov 28 2013 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE