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

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

Offset: 0

Author

Dean Hickerson, Dec 19 1999

Keywords

• sign
• easy

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• Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 15.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

Crossrefs

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

Programs

Mathematica

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

Formula

G.f.: rho(q) = Sum_{n >= 0} q^(2*n*(n+1))/((1+q+q^2)*(1+q^3+q^6)*...*(1+q^(2*n+1)+q^(4*n+2))).