OFFSET
0,9
COMMENTS
The condition that the rows be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of rows
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..209
EXAMPLE
Array begins:
====================================================================
n\k | 0 1 2 3 4 5 6
----+---------------------------------------------------------------
0 | 1 1 0 0 0 0 0 ...
1 | 1 1 1 1 1 1 1 ...
2 | 1 2 7 43 403 5245 89132 ...
3 | 1 3 28 599 23243 1440532 131530132 ...
4 | 1 5 104 6404 872681 222686668 95605470805 ...
5 | 1 7 332 57613 26560747 26852940027 52296207431182 ...
6 | 1 11 1032 473674 712725249 2776638423133 ...
7 | 1 15 2983 3599384 17328777789 ...
...
The A(2,2) = 7 matrices are:
[2 1] [2 0] [1 2] [1 1] [2 0] [1 0] [1 0]
[0 1] [0 2] [1 0] [1 0] [0 1] [1 0] [1 0]
[0 1] [0 1] [0 2] [0 1]
[0 1]
PROG
(PARI)
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
D(p, n, k)={my(v=vector(n)); for(i=1, #p, v[p[i]]++); binomial(EulerT(v)[n], k)*k!/prod(i=1, #v, i^v[i]*v[i]!)}
T(n, k)={my(m=n*k, q=Vec(exp(O(x*x^m) + intformal((x^n-1)/(1-x)))/(1-x))); if(n==0, k<=1, sum(j=0, m, my(s=0); forpart(p=j, s+=D(p, n, k), [1, n]); s*q[#q-j]))}
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Jan 10 2020
STATUS
approved