%I
%S 0,1,2,2,3,3,4,4,5,3,4,5,6,4,5,6,7,5,6,7,8,5,6,6,7,8,9,4,6,7,7,8,9,10,
%T 5,7,8,8,9,10,11,6,6,7,8,8,9,9,10,11,12,6,7,7,8,9,9,10,10,11,12,13,7,
%U 8,8,9,10,10,11,11,12
%N Number of parts of the multiset repetition class defining partition (n,k) in AbramowitzStegun order.
%C For the AbramowitzStegun (ASt) order of partitions see A036036.
%C For the first 87 multiset defining partitions in ASt order see a link under A176725.
%C This sequence is an irregular array with row length sequence A007294(n).
%F Sum(en[j],j=1..M(n)]), with the nth multiset defining partition in ASt order written as (1^en[1],2^en[2],...,M^en[M]), with M=M(n) its largest part, and positive, nonincreasing exponents en[1]>=en[2]>=...>=en[M]>=1. a(0)=0 from the empty partition defining the empty multiset.
%e Read as array:
%e 0;
%e 1;
%e 2;
%e 2,3;
%e 3,4;
%e 4,5;
%e 3,4,5,6;
%e 4,5,6,7;
%e 5,6,7,8;
%e 5,6,6,7,8,9;
%e 4, 6, 7, 7, 8, 9, 10;
%e ...,
%e linking (for row number n>=0) to the number of parts of the corresponding partitions of n.
%Y Cf. A176725, A187447.
%K nonn,easy,tabf
%O 0,3
%A _Wolfdieter Lang_, Mar 14 2011
