Search: id:A058398
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%I A058398
%S A058398 1,1,1,1,1,1,1,1,2,1,1,1,2,2,1,1,1,2,3,3,1,1,1,2,3,4,3,1,1,1,2,3,5,5,4,
%T A058398 1,1,1,2,3,5,6,7,4,1,1,1,2,3,5,7,9,8,5,1,1,1,2,3,5,7,10,11,10,5,1,1,1,
%U A058398 2,3,5,7,11,13,15,12,6,1,1,1,2,3,5,7,11,14,18,18,14,6,1,1,1,2,3,5,7,11
%N A058398 Partition triangle A008284 read from right to left.
%C A058398 a(n,m) is the number of partitions of n with n-(m-1) parts or, equivalently, 
               with greatest part n-(m-1).
%C A058398 The columns are the diagonals of triangle A008284. The diagonals are 
               the columns of the partition array p(n,m), n >= 0, m >= 1, with p(n,
               m) the number of partitions of n in which every part is <= m; p(0,
               m) := 1. For n >= 1 this array is obtained from table A026820 read 
               as lower triangular array with extension of the rows according to 
               p(n,m)=A000041(n) for m>n.
%D A058398 L. Comtet, Advanced Combinatorics, Reidel, 1974, pp. 94, 96 and 307.
%H A058398 H. Bottomley, <a href="a008284.gif">Illustration of initial terms</a>
%F A058398 a(n, m)= A008284(n, n-(m-1)).
%F A058398 a(n, m)= p(m-1, n-m+1), n >= m >= 1 with the p(n, m) array defined in 
               the comment.
%F A058398 a(n, m)=0 if n<m or m<=0 or n=0; a(1, 1)=1; a(n, m)= a(n-1, m)+a(m-1, 
               2*m-n+1).
%F A058398 Viewed as a square array by antidiagonals, T(n,k) = 0 if n<0; T(n,1) 
               = 1; otherwise T(n,k) = T(n,k-1) + T(n-k,k). - Frank Adams-Watters 
               (FrankTAW(AT)Netscape.net), Jul 25 2006
%e A058398 1; 1,1; 1,1,1; 1,1,2,1; 1,1,2,2,1;... (lower triangular matrix)
%Y A058398 Cf. A026820, A008284, A000041.
%Y A058398 Sequence in context: A086074 A089723 A055215 this_sequence A091499 A137350 
               A166240
%Y A058398 Adjacent sequences: A058395 A058396 A058397 this_sequence A058399 A058400 
               A058401
%K A058398 nonn,easy,tabl,nice
%O A058398 1,9
%A A058398 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Dec 11 
               2000

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