A118052 Number of partitions of n which contain their signature as a subpartition.

1, 1, 1, 2, 4, 5, 8, 10, 16, 22, 32, 42, 58, 75, 101, 131, 174, 223, 293, 372, 480, 607, 772, 968, 1220, 1517, 1895, 2345, 2908, 3576, 4408, 5390, 6604, 8038, 9788, 11853, 14366, 17315, 20881, 25070, 30098, 35990, 43034, 51272, 61074, 72522, 86073, 101878, 120520

Offset: 0

Author

Franklin T. Adams-Watters, Apr 10 2006

Keywords

• nonn

Comments

What is lim_{n->infinity} a(n)/p(n) (where p(n) = A000041(n) is the partition function)? It appears to be converging to something close to 0.8.

The limit must be at least 0.83846 = a(64)/p(64) and is probably closer to 0.9. - Charlie Neder, Aug 30 2018

Examples

			For n=3, signature([3]) = [1] is a subpartition of [3], signature([2,1]) = [1^2] is a subpartition of [2,1], but signature([1^3]) = [3] is not a subpartition of [1^3], so a(3)=2.
		

Links

• Charlie Neder, Table of n, a(n) for n = 0..64

Crossrefs

Cf. A000041, A115621, A115622, A000041, A118053, A118054.

Extensions

a(26) onwards from Charlie Neder, Aug 30 2018