cp's OEIS Frontend

A260413 Expansion of chi(-x) where chi() is a 3rd order mock theta function.

%I A260413 #7 Jul 25 2015 20:36:49
%S A260413 1,-1,1,0,0,0,1,-1,0,0,-1,0,1,-1,1,1,0,0,0,-1,0,0,-1,0,1,-1,1,0,-1,1,
%T A260413 1,-1,0,1,-1,0,1,-2,1,1,-1,0,1,-1,0,1,-2,0,1,-2,1,1,-1,1,1,-2,1,1,-2,
%U A260413 1,2,-2,1,1,-2,1,1,-2,0,1,-3,0,2,-3,2,2,-2,1,2
%N A260413 Expansion of chi(-x) where chi() is a 3rd order mock theta function.
%F A260413 G.f.: Sum_{k>=0} (-x)^k^2 / ((1 - x + x^2) * (1 + x^2 + x^4) ... (1 - (-x)^k + x^(2*k))).
%F A260413 a(n) = (-1)^n * A053252(n) = A260412(n) - A053251(n).
%e A260413 G.f. = 1 - x + x^2 + x^6 - x^7 - x^10 + x^12 - x^13 + x^14 + x^15 - x^19 + ...
%t A260413 a[ n_] := If[ n < 0, 0, SeriesCoefficient[ Sum[ (-x)^k^2 / Product[ 1 - (-x)^i + x^(2 i), {i, k}], {k, 0, Sqrt @ n}], {x, 0, n}]];
%o A260413 (PARI) {a(n) = if( n<0, 0, polcoeff( sum(k=0, sqrtint(n), (-x)^k^2 / prod(i=1, k, 1 - (-x)^i + x^(2*i), 1 + x * O(x^(n - k^2)))), n))};
%Y A260413 Cf. A053251, A053252, A260412.
%K A260413 sign
%O A260413 0,38
%A A260413 _Michael Somos_, Jul 24 2015