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%I #6 Sep 11 2012 19:36:38
%S 1,1,1,1,1,2,1,1,1,5,1,1,1,1,12,1,1,1,1,2,32,1,1,1,1,1,4,94,1,1,1,1,1,
%T 1,14,289,1,1,1,1,1,1,3,37,910,1,1,1,1,1,1,2,8,105,2934,1,1,1,1,1,1,1,
%U 3,18,309,9686,1,1,1,1,1,1,1,1,6,42,939,32540,1,1,1,1,1,1,1,1,1,12,100,2903
%N T(n,k)=Number of nondecreasing arrays of n 0..n-1 integers with the sum of their k'th powers equal to sum(i^k,i=0..n-1)
%C Table starts
%C .......1......1.....1....1...1..1.1.1.1
%C .......1......1.....1....1...1..1.1.1.1
%C .......2......1.....1....1...1..1.1.1.1
%C .......5......1.....1....1...1..1.1.1.1
%C ......12......2.....1....1...1..1.1.1.1
%C ......32......4.....1....1...1..1.1.1.1
%C ......94.....14.....3....2...1..1.1.1.1
%C .....289.....37.....8....3...1..1.1.1.1
%C .....910....105....18....6...1..1.1.1.1
%C ....2934....309....42...12...1..1.1.1.1
%C ....9686....939...100...24...1..2.1.1.1
%C ...32540...2903...265...63...2..2.1.1.1
%C ..110780...8865...775..164...7..2.1.1.1
%C ..381676..28163..2241..424..15..5.1.1.1
%C .1328980..90648..6709.1163..33.11.1.1.1
%C .4669367.297615.20661.2919.100.18.1.1.1
%H R. H. Hardin, <a href="/A216635/b216635.txt">Table of n, a(n) for n = 1..325</a>
%e All solutions for n=8 k=4
%e ..1....0....0
%e ..4....1....1
%e ..4....2....3
%e ..4....3....3
%e ..4....4....5
%e ..5....5....6
%e ..5....6....6
%e ..7....7....6
%Y Column 1 is A002838(n-1)
%Y sum 1..n instead of 0..n-1: A216645
%K nonn,tabl
%O 1,6
%A _R. H. Hardin_ Sep 11 2012
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