%I #17 Nov 04 2016 21:53:26
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,2,1,1,1,1,2,1,3,1,
%T 1,1,1,1,2,1,3,1,2,1,1,1,1,2,1,4,2,5,1,2,1,1,1,2,2,7,7,9,2,4,2,1,1,1,
%U 3,3,8,16,17,26,20,2,2,1,1,1,3,4,12,47,45,200,79,45,25,1,1,1,1,3,6,18,90,124
%N Table read by antidiagonals: T(n,k) is the number of strings of numbers x(i=1..n) in 0..k with sum i^4*x(i) equal to n^4*k
%C Table starts
%C .1.1.1..1...1....1.....1.....1.....1......1......1......1.......1.......1
%C .1.1.1..1...1....1.....1.....1.....1......1......1......1.......1.......1
%C .1.1.1..1...2....2.....2.....2.....2......3......3......3.......3.......3
%C .1.1.1..1...1....1.....1.....2.....3......4......6......9......11......14
%C .1.2.2..3...3....4.....7.....8....12.....18.....29.....40......60......80
%C .1.1.1..1...2....7....16....47....90....137....203....295.....412.....584
%C .1.1.2..5...9...17....45...124...307....654...1211...2023....3151....4750
%C .1.1.1..2..26..200...628..1371..2578...4737...8602..15219...25591...41530
%C .1.2.4.20..79..353..1612..5439.14366..31892..63524.118564..212692..367954
%C .1.2.2.45.860.4751.14387.34449.81289.193997.434662.897102.1742199.3234015
%H R. H. Hardin, <a href="/A184348/b184348.txt">Table of n, a(n) for n = 1..268</a>
%F T(n,k) is the coefficient of x^(k*n^4) in Product_{i=1..n} Sum_{j=0..k} x^(j*i^4). - _Robert Israel_, Nov 03 2016
%e All solutions for n=6 k=5
%e ..0....0
%e ..0....1
%e ..0....0
%e ..0....5
%e ..0....0
%e ..5....4
%p T:= (n,k) -> coeff(mul(add(x^(i^4*j),j=0..k),i=1..n),x,n^4*k):
%p seq(seq(f(n,s-n),n=1..s-1),s=2..15); # _Robert Israel_, Nov 03 2016
%Y Cf. A184339 (diagonal), A184340 - A184347 (columns 1 to 8), A184349 - A184354 (rows 3 to 8).
%K nonn,tabl
%O 1,20
%A _R. H. Hardin_, Jan 11 2011