[seqfan] n-partitions of sum of powers of 0..n-1

[Ron Hardin]

Where the infinite row of 1's will begin, vs n?
(1..n gives a similar problem, if I get to it)

T(n,k)=Number of nondecreasing arrays of 0..n-1 integers with the sum of their k 
powers equal to sum(i^k,i=0..n-1)

Table starts
........1......1....1...1.1.1.1.1.1.1.1.1.1.1.1.1.1.1
........1......1....1...1.1.1.1.1.1.1.1.1.1.1.1.1.1..
........2......1....1...1.1.1.1.1.1.1.1.1.1.1.1.1....
........5......1....1...1.1.1.1.1.1.1.1.1.1.1.1......
.......12......2....1...1.1.1.1.1.1.1.1.1.1.1........
.......32......4....1...1.1.1.1.1.1.1.1.1.1..........
.......94.....14....3...2.1.1.1.1.1.1.1..............
......289.....37....8...3.1.1.1.1.1.1................
......910....105...18...6.1.1.1.1.1..................
.....2934....309...42..12.1.1.1.1....................
.....9686....939..100..24.1.2.1......................
....32540...2903..265..63.2.2........................
...110780...8865..775.164.7..........................
...381676..28163.2241.424............................
..1328980..90648.6709................................
..4669367.297615.....................................
.16535154............................................

All solutions for n=8 k=3  
..0....0....1....0....1....2....1....0..
..0....1....1....1....4....3....2....0..
..2....1....1....2....4....4....2....0..
..4....4....2....3....4....4....3....1..
..4....5....5....4....5....4....3....2..
..6....5....6....5....5....5....3....6..
..6....5....6....6....5....6....7....6..
..6....7....6....7....6....6....7....7..


 rhhardin at mindspring.com
rhhardin at att.net (either)