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%I #4 Sep 11 2012 19:35:42
%S 1,1,1,1,1,2,1,1,1,5,1,1,1,1,12,1,1,1,1,1,32,1,1,1,1,1,3,94,1,1,1,1,1,
%T 2,8,289,1,1,1,1,1,1,2,25,910,1,1,1,1,1,1,2,6,83,2934,1,1,1,1,1,1,1,2,
%U 12,257,9686,1,1,1,1,1,1,1,1,5,30,788,32540,1,1,1,1,1,1,1,1,1,11,76,2491
%N T(n,k)=Number of nondecreasing arrays of n 1..n integers with the sum of their k powers equal to sum(i^k,i=1..n)
%C Table starts
%C .......1......1.....1....1..1..1.1
%C .......1......1.....1....1..1..1.1
%C .......2......1.....1....1..1..1.1
%C .......5......1.....1....1..1..1.1
%C ......12......1.....1....1..1..1.1
%C ......32......3.....2....1..1..1.1
%C ......94......8.....2....2..1..1.1
%C .....289.....25.....6....2..1..1.1
%C .....910.....83....12....5..1..1.1
%C ....2934....257....30...11..1..2.1
%C ....9686....788....76...25..1..2.1
%C ...32540...2491...224...51..2..2.1
%C ..110780...7885...597..136..4..2.1
%C ..381676..25099..1801..367..8..3.1
%C .1328980..80481..5469..886.21..3.1
%C .4669367.264505.16958.2507.45.14.1
%H R. H. Hardin, <a href="/A216645/b216645.txt">Table of n, a(n) for n = 1..291</a>
%e All solutions for n=8 k=4
%e ..1....1
%e ..3....2
%e ..3....3
%e ..5....4
%e ..6....5
%e ..6....6
%e ..6....7
%e ..8....8
%Y Column 1 is A002838(n-1)
%Y sum 0..n-1 instead of 1..n: A216635
%K nonn,tabl
%O 1,6
%A _R. H. Hardin_ Sep 11 2012
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