|
| |
|
|
A023871
|
|
G.f.: prod{k=1 to infty} (1 - x^k)^(-k^2).
|
|
2
| |
|
|
1, 1, 5, 14, 40, 101, 266, 649, 1593, 3765, 8813, 20168, 45649, 101591, 223654, 486046, 1045541, 2225167, 4692421, 9804734, 20318249, 41766843, 85218989, 172628766, 347338117, 694330731, 1379437080, 2724353422, 5350185097
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
LINKS
| G. Almkvist, Asymptotic formulas and generalized Dedekind sums, Exper. Math., 7 (No. 4, 1998), pp. 343-359.
|
|
|
FORMULA
| a(n)=1/n*Sum_{k=1..n} a(n-k)*sigma_3(k), n > 0, a(0)=1, where sigma_3(n)=A001158(n)=sum of cubes of divisors of n. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 20 2002
G.f : Prod{n=1 to infty} exp(sigma_3(n)*x^n/n), where sigma_3(n) is the sum of cubes of divisors of n (=A001158(n)) [From Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Mar 28 2010]
G.f. (conjectured): 1/prod(n>=1, E(x^n)^J2(n))) where E(x)=prod(n>=1,1-x^n) and J2(n)=A007434(n) [From Joerg Arndt, Jan 25 2011]
|
|
|
CROSSREFS
| Euler transform of squares (A000290).
Cf. A000219, A023872-A023878.
Sequence in context: A119996 A027089 A184437 * A171185 A122485 A198086
Adjacent sequences: A023868 A023869 A023870 * A023872 A023873 A023874
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
|
|
|
EXTENSIONS
| Definition corrected by Franklin T. Adams-Watters and R. J. Mathar, Dec 04 2006
|
| |
|
|
