A052810 1 + number of partitions of n, n>0.

1, 2, 3, 4, 6, 8, 12, 16, 23, 31, 43, 57, 78, 102, 136, 177, 232, 298, 386, 491, 628, 793, 1003, 1256, 1576, 1959, 2437, 3011, 3719, 4566, 5605, 6843, 8350, 10144, 12311, 14884, 17978, 21638, 26016, 31186, 37339, 44584, 53175, 63262, 75176, 89135

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..45.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 772

Formula

G.f.: (-x-exp(Sum(-x^j[1]/(x^j[1]-1)/j[1], j[1]=1 .. infinity))+exp(Sum(-x^j[1]/(x^j[1]-1)/j[1], j[1]=1 .. infinity))*x)/(-1+x).

a(n) = A000041(n) + A057427(n). - Alois P. Heinz, May 14 2023

Maple

spec := [S, {B=Set(C), C=Sequence(Z, 1 <= card), S=Union(C, B)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
with(combinat): A052810 := numbpart+1; [ seq(numbpart(i)+1, i=1..50) ];

Crossrefs

Cf. A000041, A057427.

Sequence in context: A125895 A241344 A064428 * A364964 A320315 A364956

Adjacent sequences: A052807 A052808 A052809 * A052811 A052812 A052813

Keyword

easy,nonn

Author

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

Extensions

Better description and more terms from Vladeta Jovovic, Oct 06 2001

Status

approved