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A260971 Expansion of phi_0(-q) in powers of q where phi_0() is a 5th order mock theta function. 0
1, -1, 1, 0, 1, -1, 0, -1, 1, -1, 1, 0, 1, -1, 1, -1, 1, -2, 1, -1, 1, -1, 1, -1, 2, -2, 2, -1, 2, -2, 1, -2, 2, -2, 2, -2, 2, -3, 2, -2, 3, -3, 3, -2, 3, -3, 3, -3, 3, -4, 4, -3, 4, -4, 3, -4, 4, -5, 4, -4, 5, -5, 5, -5, 6, -6, 5, -5, 6, -6, 6, -6, 7, -7, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,18

LINKS

Table of n, a(n) for n=0..74.

FORMULA

G.f.: Sum_{k >= 0}  (-x)^n^2 * (1 - x) * (1 - x^3) * ... * (1 - x^(2*k-1)).

a(n) = (-1)^n * A053258(n) = 2 * A053264(n) - A053262(n).

EXAMPLE

G.f. = 1 - x + x^2 + x^4 - x^5 - x^7 + x^8 - x^9 + x^10 + x^12 - x^13 + ...

G.f. = q^-1 - q^119 + q^239 + q^479 - q^599 - q^839 + q^959 - q^1079 + ...

PROG

(PARI) {a(n) = if( n<0, 0, polcoeff( sum(k=0, sqrtint(n), (-x)^k^2 * prod(i=1, k, 1 - x^(2*i - 1), 1 + x * O(x^(n - k^2)))), n))};

CROSSREFS

Cf. A053258, A053262, A053264.

Sequence in context: A031262 A047072 A178058 * A053258 A053632 A242217

Adjacent sequences:  A260968 A260969 A260970 * A260972 A260973 A260974

KEYWORD

sign

AUTHOR

Michael Somos, Aug 06 2015

STATUS

approved

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Last modified February 17 17:27 EST 2018. Contains 299296 sequences. (Running on oeis4.)