%I A059623
%S A059623 1,1,1,2,1,1,4,2,1,1,8,3,2,1,1,15,5,3,2,1,1,27,8,5,3,2,1,1,47,13,7,5,3,
%T A059623 2,1,1,79,21,11,7,5,3,2,1,1,130,33,16,11,7,5,3,2,1,1,209,52,24,15,11,7,
%U A059623 5,3,2,1,1,330,80,35,22,15,11,7,5,3,2,1,1,512,122,52,31,22,15,11,7,5,3
%N A059623 As upper right triangle, number of weakly unimodal partitions of n (weakly 
               unimodal means non-decreasing then non-increasing) where initial 
               part is k (n >= k >= 1).
%F A059623 T(n, k)=S(n, k)-S(n-k, k)+sum_j[T(n-k, j)] for j >= k, where S(n, k)=A008284(n, 
               k)=sum_j[S(n-k, j)] for n>k >= j [note reversal] with S[n, n]=1.
%e A059623 Rows are: {1,1,2,4,8,15,...}, {1,1,2,3,5,8,...}, {1,1,2,3,5,7,...} etc. 
               T(9,3)=11 since 9 can be written as 3+6, 3+5+1, 3+4+2, 3+4+1+1, 3+3+3, 
               3+3+2+1, 3+3+1+1+1, 3+2+2+2, 3+2+2+1+1, 3+2+1+1+1+1 or 3+1+1+1+1+1.
%Y A059623 Column sums give A001523. Cf. A008284, A026836, A008284, A059607, A059619.
%Y A059623 Sequence in context: A140998 A048004 A114394 this_sequence A140997 A140996 
               A141020
%Y A059623 Adjacent sequences: A059620 A059621 A059622 this_sequence A059624 A059625 
               A059626
%K A059623 nonn,tabl
%O A059623 1,4
%A A059623 Henry Bottomley (se16(AT)btinternet.com), Feb 01 2001