Search: id:A060016
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%I A060016
%S A060016 1,1,0,1,1,0,1,1,0,0,1,2,0,0,0,1,2,1,0,0,0,1,3,1,0,0,0,0,1,3,2,0,0,0,0,
%T A060016 0,1,4,3,0,0,0,0,0,0,1,4,4,1,0,0,0,0,0,0,1,5,5,1,0,0,0,0,0,0,0,1,5,7,2,
%U A060016 0,0,0,0,0,0,0,0,1,6,8,3,0,0,0,0,0,0,0,0,0,1,6,10,5,0,0,0,0,0,0,0,0,0
%N A060016 Triangle T(n,k) = number of partitions of n into k distinct parts, 1<=k<=n.
%C A060016 Also number of partitions of n-k(k+1)/2 into at most k parts (not necessarily 
               distinct).
%C A060016 A025147(n) = Sum(a(n-k+1,k-1): 1<k<=floor((n+2)/2). - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Nov 04 2007
%D A060016 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 831.
%D A060016 L. Comtet, Advanced Combinatorics, Reidel, 1974, pp. 94, 96 and 307.
%D A060016 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied 
               Tables, Cambridge, 1966, p. 219.
%D A060016 D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section XIV.2, 
               p. 493.
%H A060016 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%F A060016 T(n, k) =T(n-k, k)+T(n-k, k-1) [with T(n, 0)=1 if n=0 and 0 otherwise].
%e A060016 1; 1,0; 1,1,0; 1,1,0,0; 1,2,0,0,0; ...
%e A060016 T(8,3)=2 since 8 can be written in 2 ways as the sum of 3 distinct positive 
               integers: 5+2+1 and 4+3+1.
%Y A060016 Columns (offset) include A057427, A004526, A001399, A001400, A001401, 
               etc. Cf. A000009 (row sums), A008289 (without zeros), A030699 (row 
               maximum), A008284 (partition triangle including duplications).
%Y A060016 See A008289 for another version.
%Y A060016 Sequence in context: A025891 A120630 A089605 this_sequence A117408 A079100 
               A123262
%Y A060016 Adjacent sequences: A060013 A060014 A060015 this_sequence A060017 A060018 
               A060019
%K A060016 nonn,tabl,nice,easy
%O A060016 1,12
%A A060016 N. J. A. Sloane (njas(AT)research.att.com).
%E A060016 More terms, recurrence, etc. from Henry Bottomley (se16(AT)btinternet.com), 
               Mar 26 2001

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