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A053255 Coefficients of the '3rd order' mock theta function rho(q) 10
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

Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 15

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

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

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

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 15 04:33 EST 2018. Contains 318141 sequences. (Running on oeis4.)