|
Search: id:A006304
|
|
|
| A006304 |
|
Taylor series from Ramanujan's Lost Notebook.
(Formerly M0685)
|
|
+0
3
|
|
| 0, 1, 2, 3, 5, 8, 11, 16, 23, 31, 43, 58, 76, 101, 132, 170, 219, 280, 354, 447, 562, 699, 869, 1076, 1323, 1625, 1987, 2418, 2937, 3556, 4289, 5162, 6196, 7413, 8853, 10547, 12530, 14860, 17586, 20763, 24474, 28792, 33802, 39624, 46368, 54163
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
REFERENCES
|
G. E. Andrews, Mordell integrals and Ramanujan's "Lost" Notebook, pp. 10-48 of Analytic Number Theory (Philadelphia 1980), Lect. Notes Math. 899 (1981).
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 8.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..1000
|
|
FORMULA
|
G.f.: sum for n >= 0 of q^(n+1) (1+q^2)(1+q^4)...(1+q^(2n))/((1-q)(1-q^3)...(1-q^(2n+1)))
G.f.: sum for n >= 0 of q^(n+1)^2 (1+q)(1+q^3)...(1+q^(2n-1))/((1-q)(1-q^3)...(1-q^(2n+1)))^2
|
|
MATHEMATICA
|
Series[Sum[q^(n+1)^2 Product[1+q^(2k-1), {k, 1, n}]/Product[1-q^(2k-1), {k, 1, n+1}]^2, {n, 0, 9}], {q, 0, 100}]
|
|
CROSSREFS
|
Cf. A006305, A006306.
Sequence in context: A101018 A006336 A070228 this_sequence A039847 A046938 A060677
Adjacent sequences: A006301 A006302 A006303 this_sequence A006305 A006306 A006307
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
Corrected and extended by Dean Hickerson (dean(AT)math.ucdavis.edu), Dec 13 1999
|
|
|
Search completed in 0.002 seconds
|
