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A053262 Coefficients of the 5th order mock theta function chi_0(q) 15
1, 1, 1, 2, 1, 3, 2, 3, 3, 5, 3, 6, 5, 7, 7, 9, 7, 12, 11, 13, 13, 17, 15, 21, 20, 24, 24, 29, 28, 36, 35, 40, 42, 50, 48, 58, 58, 67, 70, 80, 79, 93, 95, 106, 111, 125, 127, 145, 149, 166, 172, 191, 196, 222, 229, 250, 262, 289, 298, 330, 343, 373, 391, 427, 442, 486 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The rank of a partition is its largest part minus the number of parts.

REFERENCES

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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 20, 23, 25

LINKS

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

George E. Andrews, The fifth and seventh order mock theta functions, Trans. Amer. Math. Soc., 293 (1986) 113-134.

George E. Andrews and Frank G. Garvan, Ramanujan's "lost" notebook VI: The mock theta conjectures, Advances in Mathematics, 73 (1989) 242-255.

George N. Watson, The mock theta functions (2), Proc. London Math. Soc., series 2, 42 (1937) 274-304.

FORMULA

G.f.: chi_0(q) = sum for n >= 0 of q^n/((1-q^(n+1))(1-q^(n+2))...(1-q^(2n)))

G.f.: chi_0(q) = 1 + sum for n >= 0 of q^(2n+1)/((1-q^(n+1))(1-q^(n+2))...(1-q^(2n+1)))

a(n) = number of partitions of 5n with rank == 1 (mod 5) minus number with rank == 0 (mod 5)

a(n) = number of partitions of n with unique smallest part and all other parts <= twice the smallest part

a(n) = number of partitions where the largest part is odd and all other parts are greater than half of the largest part [From N. Sato, Jan 21 2010]

MATHEMATICA

1+Series[Sum[q^(2n+1)/Product[1-q^k, {k, n+1, 2n+1}], {n, 0, 49}], {q, 0, 100}]

CROSSREFS

Other '5th order' mock theta functions are at A053256, A053257, A053258, A053259, A053260, A053261, A053263, A053264, A053265, A053266, A053267.

Sequence in context: A035386 A244327 A029164 * A007359 A213424 A174427

Adjacent sequences:  A053259 A053260 A053261 * A053263 A053264 A053265

KEYWORD

nonn,easy

AUTHOR

Dean Hickerson, Dec 19 1999

STATUS

approved

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Last modified May 21 20:29 EDT 2018. Contains 304400 sequences. (Running on oeis4.)