OFFSET
0,3
COMMENTS
Starting with "1" = triangle A097304 * [1, 2, 3, ...]. - Gary W. Adamson, Apr 09 2010
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
Cristina Ballantine and Mircea Merca, New convolutions for the number of divisors, Journal of Number Theory, 2016, vol. 170, pp. 17-34.
FORMULA
G.f.: G(x)*H(x) where G(x) = Sum_{k>=1} x^(2*k-1)/(1-x^(2*k-1)) is g.f. for the number of odd divisors of n (cf. A001227) and H(x) = Product_{k>=1} (1+x^k) is g.f. for the number of partitions of n into odd parts (cf. A000009). Convolution of A001227 and A000009: Sum_{k=0..n} A001227(k)*A000009(n-k). - Vladeta Jovovic, Feb 04 2002
G.f.: Sum_{n>0} n*x^n/Product_{k=1..n} (1-x^(2*k)). - Vladeta Jovovic, Dec 15 2003
a(n) ~ 3^(1/4) * (2*gamma + log(48*n/Pi^2)) * exp(Pi*sqrt(n/3)) / (8*Pi*n^(1/4)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, May 25 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Jan 31 2002
EXTENSIONS
Corrected by James A. Sellers, May 31 2007
STATUS
approved