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Number of partitions of n which contain their signature as a subpartition.
4

%I #5 Aug 30 2018 15:45:31

%S 1,1,1,2,4,5,8,10,16,22,32,42,58,75,101,131,174,223,293,372,480,607,

%T 772,968,1220,1517,1895,2345,2908,3576,4408,5390,6604,8038,9788,11853,

%U 14366,17315,20881,25070,30098,35990,43034,51272,61074,72522

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

%C 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.

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

%H Charlie Neder, <a href="/A118052/b118052.txt">Table of n, a(n) for n = 0..64</a>

%e 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.

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

%K more,nonn

%O 0,4

%A _Franklin T. Adams-Watters_, Apr 10 2006

%E a(26)-a(45) from _Charlie Neder_, Aug 30 2018