0,2

Binomial transform of A000225 (if this starts 1,1,3,7....).

Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are intersecting and for which either x is a proper subset of y or y is a proper subset of x, or 1) x = y. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 10 2008 Ross

Let P(A) be the power set of an n-element set A and R be a relation on P(A) such that for all x, y of P(A), xRy if either 0) x is not a subset of y and y is not a subset of x and x and y are disjoint, or 1) x equals y. Then a(n) = |R|. [From Ross La Haye (rlahaye(AT)new.rr.com), Mar 19 2009]

Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6. [From Ross La Haye (rlahaye(AT)new.rr.com), Feb 22 2009]

a(n)=3^n-2^n+1^n G.f. (1-4x+5x^2)/((1-x)(1-2x)(1-3x)) E.g.f. exp(3x)-exp(2x)+exp(x)

Row sums of triangle A134319. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 19 2007

a(n) = 2*StirlingS2(n+1,3) + StirlingS2(n+1,2) + 1. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 10 2008 Ross

Cf. A134319.

Cf. A028243, A000079.

Sequence in context: A148474 A156831 A027061 this_sequence A111285 A052991 A108627

Adjacent sequences: A083320 A083321 A083322 this_sequence A083324 A083325 A083326

easy,nonn

Paul Barry (pbarry(AT)wit.ie), Apr 27 2003