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A053252 Coefficients of the '3rd order' mock theta function chi(q). 8
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, 3, 0, -2, -3, -1, 2, 3, 2, -3, -3, -1, 2, 4, 1, -2, -4, -1, 3, 4, 2, -2, -4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,38

REFERENCES

Leila A. Dragonette, Some asymptotic formulas for the mock theta functions of Ramanujan, Trans. Amer. Math. Soc., 72 (1952) 474-500.

N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 55, Eq. (26.14).

Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354-355.

Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 17.

George N. Watson, The final problem: an account of the mock theta functions, J. London Math. Soc., 11 (1936) 55-80.

LINKS

Table of n, a(n) for n=0..100.

John F. R. Duncan, Michael J. Griffin and Ken Ono, Proof of the Umbral Moonshine Conjecture, arXiv:1503.01472, 2015

FORMULA

G.f.: chi(q) = sum for n >= 0 of q^n^2/((1-q+q^2)(1-q^2+q^4)...(1-q^n+q^(2n))).

G.f.: G(0), where G(k) = 1 + q^(k+1) / (1 - q^(k+1)) / G(k+1). [Joerg Arndt, Jun 29 2013]

MATHEMATICA

Series[Sum[q^n^2/Product[1-q^k+q^(2k), {k, 1, n}], {n, 0, 10}], {q, 0, 100}]

CROSSREFS

Other '3rd order' mock theta functions are at A000025, A053250, A053251, A053253, A053254, A053255, A261401.

Sequence in context: A037907 A037801 A260413 * A261029 A117195 A156606

Adjacent sequences:  A053249 A053250 A053251 * A053253 A053254 A053255

KEYWORD

sign,easy

AUTHOR

Dean Hickerson, Dec 19 1999

STATUS

approved

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Last modified December 8 01:14 EST 2016. Contains 278902 sequences.