

A006306


Taylor series from Ramanujan's Lost Notebook.
(Formerly M0163)


4



1, 1, 1, 2, 1, 4, 1, 5, 2, 5, 4, 7, 4, 11, 3, 13, 6, 14, 9, 18, 7, 24, 8, 29, 14, 32, 17, 38, 18, 50, 20, 58, 25, 63, 33, 77, 35, 94, 36, 108, 48, 122, 60, 141, 63, 170, 70, 195, 87, 215, 101, 250, 110, 294, 124, 333, 146, 371, 173, 424, 190, 492, 206, 554, 245, 617, 283
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OFFSET

0,4


COMMENTS

Contribution from Jeremy Lovejoy, Dec 19 2008: (Start)
Coefficients of the "second order" mock theta function mu(q).
a(n) is the number of partitions of n without repeated odd parts whose M2rank is even minus the number of partitions of n without repeated odd parts whose M2rank is odd. (End)


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000
G. E. Andrews, Mordell integrals and Ramanujan's "Lost" Notebook, pp. 1048 of Analytic Number Theory (Philadelphia 1980), Lect. Notes Math. 899 (1981).
K. Bringmann, K. Ono and R. Rhoades, Eulerian series as modular forms, J. Amer. Math. Soc. 21 (2008), 10851104. [From Jeremy Lovejoy, Dec 19 2008]
J. Lovejoy and R. Osburn, M_2rank differences for partitions without repeated odd parts [From Jeremy Lovejoy, Dec 19 2008]
R. J. McIntosh, Second order mock theta functions, Canad. Math. Bull. 50 (2007), 284290. [From Jeremy Lovejoy, Dec 19 2008]


FORMULA

G.f.: sum for n >= 0 of (1)^n q^n^2 (1q)(1q^3)...(1q^(2n1))/((1+q^2)^2 (1+q^4)^2 ... (1+q^(2n))^2)


MATHEMATICA

CoefficientList[Series[Sum[(q)^n^2 Product[(1q^(2k1))/(1+q^(2k))^2, {k, 1, n}], {n, 0, 10}], {q, 0, 100}], q]


CROSSREFS

Cf. A006304, A006305.
Sequence in context: A102627 A088296 A093890 * A214579 A083711 A018783
Adjacent sequences: A006303 A006304 A006305 * A006307 A006308 A006309


KEYWORD

sign,easy,nice,changed


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Corrected and extended by Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 13 1999


STATUS

approved



