A362644 Array read by antidiagonals: T(n,k) is the number of nonisomorphic multisets of permutations of an n-set with k permutations.
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 8, 5, 1, 1, 1, 5, 17, 28, 7, 1, 1, 1, 6, 34, 159, 96, 11, 1, 1, 1, 7, 61, 888, 2655, 495, 15, 1, 1, 1, 8, 105, 4521, 76854, 88885, 2919, 22, 1, 1, 1, 9, 170, 20916, 1882581, 15719714, 4255594, 22024, 30, 1
Offset: 0
Examples
Array begins: ==================================================================== n/k| 0 1 2 3 4 5 6 ... ---+---------------------------------------------------------------- 0 | 1 1 1 1 1 1 1 ... 1 | 1 1 1 1 1 1 1 ... 2 | 1 2 3 4 5 6 7 ... 3 | 1 3 8 17 34 61 105 ... 4 | 1 5 28 159 888 4521 20916 ... 5 | 1 7 96 2655 76854 1882581 39122096 ... 6 | 1 11 495 88885 15719714 2271328951 274390124129 ... 7 | 1 15 2919 4255594 5341866647 5387750530872 4530149870111873 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals).
Crossrefs
Programs
-
PARI
B(n,k) = {n!*k^n} K(v)=my(S=Set(v)); prod(i=1, #S, my(k=S[i], c=#select(t->t==k, v)); B(c, k)) R(v, m)=concat(vector(#v, i, my(t=v[i], g=gcd(t, m)); vector(g, i, t/g))) permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m} T(n,k) = {if(n==0, 1, my(s=0); forpart(q=n, s += permcount(q) * polcoef(exp(sum(m=1, k, K(R(q,m))*x^m/m, O(x*x^k))), k)); s/n!)}
Formula
T(0,k) = T(1,k) = 1.
Comments