A052839 Number of partitions of n into distinct summands (A000009), plus 1 (apart from the first term).

1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 11, 13, 16, 19, 23, 28, 33, 39, 47, 55, 65, 77, 90, 105, 123, 143, 166, 193, 223, 257, 297, 341, 391, 449, 513, 586, 669, 761, 865, 983, 1114, 1261, 1427, 1611, 1817, 2049, 2305, 2591, 2911, 3265, 3659, 4098, 4583, 5121, 5719, 6379

Offset

0,2

Links

Table of n, a(n) for n=0..55.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 806

Formula

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

Maple

spec := [S, {C=Sequence(Z, 1 <= card), B=PowerSet(C), S=Union(B, C)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..67);
Or: with(gfun, seriestolist); seriestolist(series(mul(1+z^i, i=1..81)+z/(1-z), z, 81));

Mathematica

a[n_] := If[n == 0, 1, PartitionsQ[n] + 1];
a /@ Range[0, 55] (* Jean-François Alcover, May 07 2020 *)

Crossrefs

Apart from the first term equals A000009 + 1 and also the left edge of A068049.

Sequence in context: A125890 A067661 A210024 * A125894 A091493 A305148

Adjacent sequences: A052836 A052837 A052838 * A052840 A052841 A052842

Keyword

easy,nonn

Author

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

Extensions

Edited by Antti Karttunen, Feb 13 2002, based on information received from Bruno Salvy.

Status

approved