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A052810 a(n) = 1 + (number of partitions of n, n>0).

%I A052810 #37 Jun 21 2024 11:00:19
%S A052810 1,2,3,4,6,8,12,16,23,31,43,57,78,102,136,177,232,298,386,491,628,793,
%T A052810 1003,1256,1576,1959,2437,3011,3719,4566,5605,6843,8350,10144,12311,
%U A052810 14884,17978,21638,26016,31186,37339,44584,53175,63262,75176,89135
%N A052810 a(n) = 1 + (number of partitions of n, n>0).
%C A052810 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 A052810 Paolo Xausa, <a href="/A052810/b052810.txt">Table of n, a(n) for n = 0..10000</a>
%H A052810 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=772">Encyclopedia of Combinatorial Structures 772</a>.
%F A052810 G.f.: exp(Sum_{j >= 1} (x^j)/(1 - x^j)/j) - x/(x - 1). [Simplified by _Paolo Xausa_, Jun 21 2024]
%F A052810 a(n) = A000041(n) + A057427(n). - _Alois P. Heinz_, May 14 2023
%p A052810 spec := [S,{B=Set(C),C=Sequence(Z,1 <= card), S = Union(C,B)}, unlabeled]:
%p A052810 seq(combstruct[count](spec, size=n), n=0..20);
%p A052810 A052810 := n -> combinat:-numbpart(n) + ifelse(n=0, 0, 1):
%p A052810 seq(A052810(i), i=0..50);
%t A052810 Join[{1}, PartitionsP[Range[50]] + 1] (* _Paolo Xausa_, Jun 21 2024 *)
%Y A052810 Cf. A000041, A057427.
%K A052810 easy,nonn
%O A052810 0,2
%A A052810 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052810 Better description and more terms from _Vladeta Jovovic_, Oct 06 2001