Search: id:A092905
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%I A092905
%S A092905 1,1,1,1,2,1,1,3,2,1,1,4,4,2,1,1,5,6,4,2,1,1,6,9,7,4,2,1,1,7,12,11,7,4,
%T A092905 2,1,1,8,16,16,12,7,4,2,1,1,9,20,23,18,12,7,4,2,1,1,10,25,31,27,19,12,
               7,
%U A092905 4,2,1,1,11,30,41,38,29,19,12,7,4,2,1,1,12,36,53,53,42,30,19,12,7,4,2,
               1
%N A092905 Triangle, read by rows, such that the partial sums of the n-th row form 
               the n-th diagonal, for n>=0, where each row begins with 1.
%C A092905 Row sums form A000070, which is the partial sums of the partition numbers 
               (A000041). Rows read backwards converge to the row sums (A000070).
%F A092905 T(n, k) = sum_{j=0..k} T(n-k, j), with T(0, n) = 1 for all n>=0. A000070(n) 
               = sum_{k=0..n} T(n, k).
%F A092905 E.g.f.: (1/(1-y))*(1/Product(1-x*y^k, k=1..infinity)). - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Jan 29 2005
%e A092905 The third row is {1,3,2,1} and the third diagonal is the partial sums 
               of the third row: {1,4,6,7,7,7,7,7,...}.
%e A092905 Rows begin:
%e A092905 {1},
%e A092905 {1,1},
%e A092905 {1,2,1},
%e A092905 {1,3,2,1},
%e A092905 {1,4,4,2,1},
%e A092905 {1,5,6,4,2,1},
%e A092905 {1,6,9,7,4,2,1},
%e A092905 {1,7,12,11,7,4,2,1},
%e A092905 {1,8,16,16,12,7,4,2,1},
%e A092905 {1,9,20,23,18,12,7,4,2,1},
%e A092905 {1,10,25,31,27,19,12,7,4,2,1},
%e A092905 {1,11,30,41,38,29,19,12,7,4,2,1},
%e A092905 {1,12,36,53,53,42,30,19,12,7,4,2,1},...
%p A092905 T(n,k)=if(n<k|k<0,0,if(n==k|k==0,1,sum(j=0,min(k,n-k),T(n-k,j))))
%Y A092905 Antidiagonal sums form the partition numbers (A000041).
%Y A092905 Cf. A000070.
%Y A092905 Sequence in context: A136575 A077592 A055794 this_sequence A052509 A093628 
               A114282
%Y A092905 Adjacent sequences: A092902 A092903 A092904 this_sequence A092906 A092907 
               A092908
%K A092905 nonn,tabl
%O A092905 0,5
%A A092905 Paul D. Hanna (pauldhanna(AT)juno.com), Mar 12 2004

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