1,6

Number of partitions of n-1 with at least two parts of size 2 or larger. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 13 2006

Also equal to the number of partitions p of n-1 such that max(p)-min(p) > 1. Example: a(7)=5 because we have [5,1],[4,2],[4,1,1],[3,2,1] and [3,1,1,1]. - Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 06 2006 END Also number of partitions of n-1 with at least two parts that are smaller than the largest part. Example: a(7)=5 because we have [4,1,1],[3,2,1],[3,1,1,1],[2,2,1,1,1] and [2,1,1,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 01 2006

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

Christian G. Bower, Table of n, a(n) for n=1..500

Index entries for sequences related to trees

G.f.=x/product(1-x^j,j=1..infinity)-x-x^2/(1-x)^2. G.f.=sum(sum(x^(i+j+1)/product(1-x^k, k=i..j), i=1..j-2), j=3..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 01 2006

g:=x/product(1-x^j, j=1..70)-x-x^2/(1-x)^2: gser:=series(g, x=0, 48): seq(coeff(gser, x, n), n=1..46); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 01 2006

a(n+1)=A000041(n)-n for n>0 - John W. Layman (layman(AT)math.vt.edu)

Adjacent sequences: A000091 A000092 A000093 this_sequence A000095 A000096 A000097

Sequence in context: A022907 A006918 A011842 this_sequence A058578 A023674 A139218

nonn

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 13 2006