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A260413
Expansion of chi(-x) where chi() is a 3rd order mock theta function.
1
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
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
KEYWORD
sign
AUTHOR
Michael Somos, Jul 24 2015
STATUS
approved