A052810 - OEIS

%I #37 Jun 21 2024 11:00:19

%S 1,2,3,4,6,8,12,16,23,31,43,57,78,102,136,177,232,298,386,491,628,793,

%T 1003,1256,1576,1959,2437,3011,3719,4566,5605,6843,8350,10144,12311,

%U 14884,17978,21638,26016,31186,37339,44584,53175,63262,75176,89135

%N a(n) = 1 + (number of partitions of n, n>0).

%C For n>0: number of occurrences of n in partitions of 2*n: a(n)=A066633(2*n,n), cf. A058696. - _Reinhard Zumkeller_, Feb 22 2004

%H Paolo Xausa, <a href="/A052810/b052810.txt">Table of n, a(n) for n = 0..10000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=772">Encyclopedia of Combinatorial Structures 772</a>.

%F G.f.: exp(Sum_{j >= 1} (x^j)/(1 - x^j)/j) - x/(x - 1). [Simplified by _Paolo Xausa_, Jun 21 2024]

%F a(n) = A000041(n) + A057427(n). - _Alois P. Heinz_, May 14 2023

%p spec := [S,{B=Set(C),C=Sequence(Z,1 <= card), S = Union(C,B)}, unlabeled]:

%p seq(combstruct[count](spec, size=n), n=0..20);

%p A052810 := n -> combinat:-numbpart(n) + ifelse(n=0, 0, 1):

%p seq(A052810(i), i=0..50);

%t Join[{1}, PartitionsP[Range[50]] + 1] (* _Paolo Xausa_, Jun 21 2024 *)

%Y Cf. A000041, A057427.

%K easy,nonn

%O 0,2

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000

%E Better description and more terms from _Vladeta Jovovic_, Oct 06 2001