A015724 Number of parts in all partitions of all the numbers in {1,2,...,n} into distinct parts.
1, 2, 5, 8, 13, 21, 31, 44, 62, 87, 117, 157, 206, 269, 349, 447, 566, 715, 894, 1112, 1378, 1696, 2076, 2531, 3072, 3712, 4472, 5367, 6417, 7651, 9093, 10772, 12732, 15004, 17639, 20691, 24211, 28265, 32934, 38293, 44435, 51470, 59507, 68677
Offset: 1
Keywords
Formula
Partial sums of A015723.
G.f.: (1/(1 - x)) * Sum_{i>=1} x^i/(1 + x^i) * Product_{j>=1} (1 + x^j). - Ilya Gutkovskiy, Apr 04 2017
a(n) ~ 3^(3/4) * log(2) * exp(Pi*sqrt(n/3)) * n^(1/4) / Pi^2. - Vaclav Kotesovec, Jun 20 2025
Extensions
Corrected by Vladeta Jovovic, Dec 03 2004