%I A097306
%S A097306 1,1,1,2,1,2,1,2,3,1,3,4,1,3,4,5,1,3,5,6,1,4,6,7,8,1,4,7,9,10,1,4,8,10,
%T A097306 11,12,1,5,9,12,14,15,1,5,10,14,16,17,18,1,5,11,16,19,21,22,1,6,13,19,
%U A097306 23,25,26,27,1,6,14,21,26,29,31,32,1,6,15,24,30,34,36,37,38,1,7,17,27
%N A097306 Array of number of partitions of n with odd parts not exceeding 2*m-1 
               with m in {1,2,..., ceiling(n/2)}.
%C A097306 The sequence of row lengths of this array is A008619 = [1,1,2,2,3,3,4,
               4,5,5,6,6,7,7,...].
%C A097306 This is the partial row sums array of array A097305.
%C A097306 The number of partitions of N=2*n (n>=1) into even parts not exceeding 
               2*k,with k from {1,..,n}, is given by the triangle A026820(n,k).
%H A097306 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A097306.text">
               First 18 rows</a>.
%F A097306 T(n, m)= number of partitions of n with odd parts only and largest parts 
               <= 2*m-1 for m from {1, 2, ..., ceiling(n/2)}.
%F A097306 T(n, m)= sum(A097305(n, k), k=1..m), m=1..ceiling(n/2), n>=1.
%e A097306 [1]; [1]; [1,2]; [1,2]; [1,2,3]; [1,3,4]; [1,3,4,5]; [1,3,5,6]; ...
%e A097306 T(8,2)=3 because there are three partitions of 8 with odd parts not exceeding 
               3, namely (1^8), (1^5,3) and (1^2,3^2).
%e A097306 T(6,2)=3 from the partitions (1^6), (1^3,3) and (3^2).
%p A097306 Sequence of row numbers for n>=1: [seq(coeff(series(product(1/(1-x^(2*k-1)),
               k=1..p),x,n+1),x,n),p=1..ceil(n/2))].
%Y A097306 Row sums: A097307.
%Y A097306 Sequence in context: A030718 A028334 A083269 this_sequence A102632 A094076 
               A089611
%Y A097306 Adjacent sequences: A097303 A097304 A097305 this_sequence A097307 A097308 
               A097309
%K A097306 nonn,tabf,easy
%O A097306 1,4
%A A097306 Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), 
               Aug 13 2004