%I A059619
%S A059619 1,1,1,1,0,1,3,1,1,1,4,2,0,1,1,6,2,1,1,1,1,10,4,2,1,1,1,1,15,6,3,1,2,1,
%T A059619 1,1,21,9,4,2,1,2,1,1,1,30,12,6,3,2,2,2,1,1,1,43,18,8,5,3,2,2,2,1,1,1,
%U A059619 59,25,12,6,3,3,3,2,2,1,1,1,82,34,17,9,5,4,3,3,2,2,1,1,1,111,48,22,12
%N A059619 As upper right triangle, number of strongly unimodal partitions of n 
               (strongly unimodal means strictly increasing then strictly decreasing) 
               where initial part is k.
%F A059619 T(n, k)=S(n, k)+sum_j[T(n-k, j)] for j>k, where S(n, k)=A059607(n, k)=sum_j[S(n-k, 
               j)] for k>j [note reversal] with S(0, 0)=1.
%e A059619 Rows start: {1,1,1,3,4,6,...}, {1,0,1,2,...}, {1,1,0,...} etc. T(16,6)=8 
               since 16 can be written as 6+10, 6+9+1, 6+8+2, 6+7+3, 6+7+2+1, 6+5+4+1, 
               6+5+3+2, or 6+4+3+2+1 (but for example neither 6+6+4 nor 6+8+1+1 
               which are only weakly unimodal).
%Y A059619 Top row is A059618 and is sum of other rows (for n>0). Cf. A000009, A000041, 
               A001523, A059607.
%Y A059619 Sequence in context: A079110 A079619 A157603 this_sequence A098950 A123940 
               A101021
%Y A059619 Adjacent sequences: A059616 A059617 A059618 this_sequence A059620 A059621 
               A059622
%K A059619 nonn,tabl
%O A059619 0,7
%A A059619 Henry Bottomley (se16(AT)btinternet.com), Jan 31 2001