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%I #10 May 08 2018 15:11:55
%S 1,2,1,3,3,1,4,6,6,4,1,5,10,10,10,10,5,1,6,15,15,15,20,20,20,15,15,6,
%T 1,7,21,21,21,35,35,35,35,35,35,35,21,21,7,1,8,28,28,28,28,56,56,56,
%U 56,56,70,70,70,70,70,56,56,56,28,28,8,1,9,36,36,36,36,84,84,84,84,84,84,84
%N Table read by rows: row n has a term T(n,k) for each of the partition(n) partitions of n. T(n,k) = binomial(n,m) where m is the number of parts.
%C A035206 and A036038 were used to generate A049009 (Words over signatures). A098346 and A049019 provide another approach to the same end since A098346 times A049019 also yields A049009. (cf. A000312 and A000670).
%C Partitions are in Abramowitz and Stegun order. - _Franklin T. Adams-Watters_, Nov 20 2006
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%F a(n) = Combin( A036042(n), A036043(n) )
%e A036042 begins 1 2 2 3 3 3 4 4 4 4 4 ...
%e A036043 begins 1 1 2 1 2 3 1 2 2 3 4 ...
%e so a(n) begins 1 2 1 3 3 1 4 6 6 4 1 ...
%Y Cf. A090657, A000041 (row lengths), A098545 (row sums), A036036, A036042, A036043.
%K easy,nonn,tabf
%O 1,2
%A _Alford Arnold_, Sep 14 2004
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