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A053255 Coefficients of the '3rd order' mock theta function rho(q) 8
1, -1, 0, 1, 0, -1, 1, -1, 0, 1, -1, 0, 2, -1, -1, 1, -1, -1, 2, -1, 0, 2, -1, -1, 2, -2, -1, 3, -2, -1, 3, -2, -1, 3, -2, -1, 4, -3, -1, 4, -2, -2, 4, -3, -2, 5, -4, -2, 6, -3, -2, 6, -4, -2, 7, -5, -2, 7, -5, -3, 8, -6, -3, 9, -6, -3, 10, -6, -4, 10, -7, -4, 12, -8, -4, 13, -8, -5, 13, -9, -5, 15, -10, -5, 16, -11, -6, 17, -12, -7, 19, -13, -6, 21, -13 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

REFERENCES

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

Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 15

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..94.

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

FORMULA

G.f.: rho(q) = sum for n >= 0 of q^(2n(n+1))/((1+q+q^2)(1+q^3+q^6)...(1+q^(2n+1)+q^(4n+2)))

MATHEMATICA

Series[Sum[q^(2n(n+1))/Product[1+q^(2k+1)+q^(4k+2), {k, 0, n}], {n, 0, 6}], {q, 0, 100}]

CROSSREFS

Other '3rd order' mock theta functions are at A000025, A053250, A053251, A053252, A053253, A053254.

Sequence in context: A237717 A154338 A087436 * A085856 A132126 A031264

Adjacent sequences:  A053252 A053253 A053254 * A053256 A053257 A053258

KEYWORD

sign,easy

AUTHOR

Dean Hickerson, Dec 19 1999

STATUS

approved

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Last modified December 9 12:25 EST 2016. Contains 278971 sequences.