1,2

Also the number of one-element transitions from the integer partitions of n to the partitions of n-1 for labeled parts with the assumption that any part z is composed of labeled elements of amount 1, i.e. z = 1_1 + 1_2 +... + 1_z. Then one can take from z a single element in z different ways. E.g. for n=3 to n=2 we have A066186(3) = 9 and [111] --> [11], [111] --> [11], [111] --> [11], [12] --> [111], [12] --> [111], [12] --> [2], [3] --> 2, [3] --> 2, [3] --> 2. For the unlabeled case, one can take a single element from z in only one way. Then the number of one-element transitions from the integer partitions of n to the partitions of n-1 is given by A000070. E.g. A000070(3) = 4 and for the transition from n=3 to n=2 one has [111] --> [11], [12] --> [11], [12] --> [2], [3] --> [2]. - Thomas Wieder (wieder.thomas(AT)t-online.de), May 20 2004

G.f. = d/dx [Product_{k>0} 1/(1-x^k)], i.e. derivative of g.f. for A000041. - Jon Perry (perry(AT)globalnet.co.uk), Mar 17 2004

Equals A132825 * [1, 2, 3,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 02 2007

a(n)= n PartitionsP[n]

a:=n->sum(numbpart (n), j=1..n): seq(a(n), n=1..38); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007

seq(k*numbpart(k), k=1..38) ; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 06 2007

PartitionsP[ Range[ 60 ] ]Range[ 60 ]

Cf. A093694, A000070.

Cf. A132825.

Sequence in context: A075385 A048150 A164931 this_sequence A059403 A009909 A009910

Adjacent sequences: A066183 A066184 A066185 this_sequence A066187 A066188 A066189

easy,nonn

Wouter Meeussen (wouter.meeussen(AT)pandora.be), Dec 15 2001