login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A260460 Expansion of f(-q) in powers of q where f() is a 3rd order mock theta function. 0

%I

%S 1,-1,-2,-3,-3,-3,-5,-7,-6,-6,-10,-12,-11,-13,-17,-20,-21,-21,-27,-34,

%T -33,-36,-46,-51,-53,-58,-68,-78,-82,-89,-104,-118,-123,-131,-154,

%U -171,-179,-197,-221,-245,-262,-279,-314,-349,-369,-398,-446,-486,-515,-557

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

%F G.f.: Sum_{k>=0} (-x)^(k^2) / Product_{i=1..k} (1 + (-x)^i)^2.

%F 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 a(n) = (-1)^n * A000025(n). a(n) < 0 if n>0.

%F a(n) = A053250(n) - 2 * A053251(n) = 2 * A053250(n) - A132969(n) = A132969(n) - 4 * A053251(n).

%e 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 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 (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 Cf. A000025, A053250, A053251, A132969.

%K sign

%O 0,3

%A _Michael Somos_, Jul 26 2015

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 24 11:26 EDT 2021. Contains 348225 sequences. (Running on oeis4.)