cp's OEIS Frontend

A260460 Expansion of f(-q) in powers of q where f() is a 3rd order mock theta function.

%I A260460 #5 Jul 26 2015 15:19:20
%S A260460 1,-1,-2,-3,-3,-3,-5,-7,-6,-6,-10,-12,-11,-13,-17,-20,-21,-21,-27,-34,
%T A260460 -33,-36,-46,-51,-53,-58,-68,-78,-82,-89,-104,-118,-123,-131,-154,
%U A260460 -171,-179,-197,-221,-245,-262,-279,-314,-349,-369,-398,-446,-486,-515,-557
%N A260460 Expansion of f(-q) in powers of q where f() is a 3rd order mock theta function.
%F A260460 G.f.: Sum_{k>=0} (-x)^(k^2) / Product_{i=1..k} (1 + (-x)^i)^2.
%F A260460 G.f.: 2 * (Sum_{k in Z} (-1)^k * x^(k*(3*k + 1)/2) / (1 + x^k)) / (Sum_{k in Z} (-1)^k * x^(k*(3*k + 1)/2))
%F A260460 a(n) = (-1)^n * A000025(n). a(n) < 0 if n>0.
%F A260460 a(n) = A053250(n) - 2 * A053251(n) = 2 * A053250(n) - A132969(n) = A132969(n) - 4 * A053251(n).
%e A260460 G.f. = 1 - x - 2*x^2 - 3*x^3 - 3*x^4 - 3*x^5 - 5*x^6 - 7*x^7 - 6*x^8 + ...
%t A260460 a[ n_] := If[ n < 0, 0, SeriesCoefficient[ Sum[ (-x)^k^2 / Product[ 1 + (-x)^j, {j, k}]^2, {k, 0, Sqrt@n}], {x, 0, n}]];
%o A260460 (PARI) {a(n) = my(t); if( n<0, 0, t = 1 + O(x^n); polcoeff( sum(k=1, sqrtint(n), t *= (-x)^(2*k - 1) / (1 + (-x)^k)^2 + x * O(x^(n - (k-1)^2)), 1), n))};
%Y A260460 Cf. A000025, A053250, A053251, A132969.
%K A260460 sign
%O A260460 0,3
%A A260460 _Michael Somos_, Jul 26 2015