|
Search: id:A006305
|
|
|
| A006305 |
|
Taylor series related to one in Ramanujan's Lost Notebook.
(Formerly M1014)
|
|
+0
3
|
|
| 1, 2, 4, 6, 10, 16, 25, 38, 58, 84, 122, 174, 244, 338, 465, 630, 850, 1136, 1508, 1988, 2608, 3398, 4408, 5688, 7306, 9342, 11900, 15090, 19070, 24008, 30122, 37666, 46955, 58348, 72302, 89338, 110094, 135316, 165912, 202924, 247632, 301508
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
G. E. Andrews, Mordell integrals and Ramanujan's "Lost" Notebook, pp. 10-48 of Analytic Number Theory (Philadelphia 1980), Lect. Notes Math. 899 (1981).
|
|
FORMULA
|
G.f.: sum for n >= 0 of q^(n^2+n) (1+q^2)(1+q^4)...(1+q^(2n))/((1-q)^2 (1-q^2) (1-q^3)^2 (1-q^4) ... (1-q^(2n)) (1-q^(2n+1))^2)
|
|
MATHEMATICA
|
Series[Sum[q^(n^2+n)/(1-q)^2 Product[(1+q^(2k))/((1-q^(2k))(1-q^(2k+1))^2), {k, 1, n}], {n, 0, 9}], {q, 0, 100}]
|
|
CROSSREFS
|
Cf. A006304, A006306.
Adjacent sequences: A006302 A006303 A006304 this_sequence A006306 A006307 A006308
Sequence in context: A098151 A132002 A028445 this_sequence A067247 A017985 A028488
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
Corrected and extended by Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 13 1999
|
|
|
Search completed in 0.002 seconds
|
