|
| |
|
|
A053276
|
|
Coefficients of the '7th order' mock theta function F_1(q)
|
|
12
| |
|
|
0, 1, 1, 1, 2, 1, 2, 2, 2, 3, 3, 2, 4, 4, 4, 4, 6, 5, 6, 6, 7, 8, 9, 8, 10, 11, 11, 12, 14, 13, 16, 16, 18, 19, 21, 20, 24, 25, 26, 28, 31, 31, 35, 36, 39, 41, 45, 45, 50, 53, 55, 58, 64, 65, 71, 73, 79, 83, 89, 90, 99, 103, 109, 114, 123, 126, 135, 141, 149, 157, 167, 171, 185
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
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
Dean Hickerson, On the seventh order mock theta functions, Inventiones Mathematicae, 94 (1988) 661-677
Srinivasa Ramanujan, Collected Papers, Chelsea, New York, 1962, pp. 354-355
Atle Selberg, Uber die Mock-Thetafunktionen siebenter Ordnung, Arch. Math. Naturvidenskab, 41 (1938) 3-15
|
|
|
FORMULA
| G.f.: F_1(q) = sum for n >= 1 of q^n^2/((1-q^n)(1-q^(n+1))...(1-q^(2n-1)))
a(n) = number of partitions of 7n-1 with rank == 2 (mod 7) minus number with rank == 3 (mod 7)
|
|
|
MATHEMATICA
| Series[Sum[q^n^2/Product[1-q^k, {k, n, 2n-1}], {n, 1, 10}], {q, 0, 100}]
|
|
|
CROSSREFS
| Other '7th order' mock theta functions are at A053275, A053277, A053278, A053279, A053280.
Sequence in context: A120254 A068796 A154804 * A064065 A054705 A025800
Adjacent sequences: A053273 A053274 A053275 * A053277 A053278 A053279
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999
|
| |
|
|
