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A053262 Coefficients of the 5th order mock theta function chi_0(q) 11
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

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

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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 20, 23, 25

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

LINKS

Table of n, a(n) for n=0..65.

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 November 27 04:09 EST 2014. Contains 250155 sequences.