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.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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)

Sequence in context: A006918 A165189 A011842 this_sequence A058578 A023674 A139218

Adjacent sequences: A000091 A000092 A000093 this_sequence A000095 A000096 A000097

nonn

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

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