|
| |
|
|
A053263
|
|
Coefficients of the '5th order' mock theta function chi_1(q)
|
|
11
| |
|
|
1, 2, 2, 3, 3, 4, 4, 6, 5, 7, 8, 9, 9, 12, 12, 15, 15, 18, 19, 23, 23, 27, 30, 33, 34, 41, 42, 49, 51, 57, 61, 69, 72, 81, 87, 96, 100, 113, 119, 132, 140, 153, 163, 180, 188, 208, 221, 240, 253, 278, 294, 319, 339, 366, 388, 422, 443, 481, 510, 549, 580, 626, 662
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 20, 25
George N. Watson, The mock theta functions (2), Proc. London Math. Soc., series 2, 42 (1937) 274-304
|
|
|
FORMULA
| G.f.: chi_1(q) = sum for n >= 0 of q^n/((1-q^(n+1))(1-q^(n+2))...(1-q^(2n+1)))
G.f.: chi_1(q) = 1 + sum for n >= 0 of q^(2n+1) (1+q^n)/((1-q^(n+1))(1-q^(n+2))...(1-q^(2n+1)))
a(n) = twice the number of partitions of 5n+3 with rank == 2 (mod 5) minus number with rank == 0 or 1 (mod 5)
a(n) - 1 = number of partitions of n with unique smallest part and all other parts <= one plus twice the smallest part
|
|
|
MATHEMATICA
| 1+Series[Sum[q^(2n+1)(1+q^n)/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, A053262, A053264, A053265, A053266, A053267.
Sequence in context: A030699 A083802 A100881 * A056039 A034322 A058747
Adjacent sequences: A053260 A053261 A053262 * A053264 A053265 A053266
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999
|
| |
|
|
