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

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, 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, 1, 2, -2, 1, 1, -2, 1, 1, -2, 0, 1, -3, 0, 2, -3, 2, 2, -2, 1, 2

Offset

0,38

Links

Table of n, a(n) for n=0..78.

Formula

G.f.: Sum_{k>=0} (-x)^k^2 / ((1 - x + x^2) * (1 + x^2 + x^4) ... (1 - (-x)^k + x^(2*k))).

a(n) = (-1)^n * A053252(n) = A260412(n) - A053251(n).

Example

G.f. = 1 - x + x^2 + x^6 - x^7 - x^10 + x^12 - x^13 + x^14 + x^15 - x^19 + ...

Mathematica

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}]];

Prog

(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))};

Crossrefs

Cf. A053251, A053252, A260412.

Sequence in context: A365167 A037801 A340219 * A053252 A261029 A117195

Adjacent sequences: A260410 A260411 A260412 * A260414 A260415 A260416

Keyword

sign

Author

Michael Somos, Jul 24 2015

Status

approved