|
| |
|
|
A053264
|
|
Coefficients of the '5th order' mock theta function F_0(q)
|
|
11
| |
|
|
1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6, 6, 7, 8, 8, 10, 11, 11, 13, 14, 15, 17, 18, 19, 22, 24, 25, 28, 30, 32, 36, 39, 41, 45, 49, 52, 57, 61, 65, 71, 76, 81, 88, 94, 100, 109, 116, 123, 133, 142, 151, 163, 174, 184, 198, 211, 224, 240, 255, 271, 290
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,9
|
|
|
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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 20, 22, 23, 25
George N. Watson, The mock theta functions (2), Proc. London Math. Soc., series 2, 42 (1937) 274-304
|
|
|
FORMULA
| G.f.: F_0(q) = sum for n >= 0 of q^(2n^2)/((1-q)(1-q^3)...(1-q^(2n-1)))
a(n) = number of partitions of n into odd parts, each of which occurs at least twice, such that if k occurs then all smaller positive odd numbers occur
|
|
|
MATHEMATICA
| Series[Sum[q^(2n^2)/Product[1-q^(2k+1), {k, 0, n-1}], {n, 0, 7}], {q, 0, 100}]
|
|
|
CROSSREFS
| Other '5th order' mock theta functions are at A053256, A053257, A053258, A053259, A053260, A053261, A053262, A053263, A053265, A053266, A053267.
Sequence in context: A099199 A172474 A062276 * A079440 A192262 A026414
Adjacent sequences: A053261 A053262 A053263 * A053265 A053266 A053267
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999
|
| |
|
|
