A320801 Regular triangle read by rows where T(n,k) is the number of nonnegative integer matrices up to row and column permutations with no zero rows or columns and k nonzero entries summing to n.
1, 0, 1, 0, 1, 3, 0, 1, 3, 6, 0, 1, 6, 10, 16, 0, 1, 6, 20, 30, 34, 0, 1, 9, 31, 75, 92, 90, 0, 1, 9, 45, 126, 246, 272, 211, 0, 1, 12, 60, 223, 501, 839, 823, 558, 0, 1, 12, 81, 324, 953, 1900, 2762, 2482, 1430, 0, 1, 15, 100, 491, 1611, 4033, 7120, 9299, 7629, 3908
Offset: 0
Examples
Triangle begins: 1 0 1 0 1 3 0 1 3 6 0 1 6 10 16 0 1 6 20 30 34 0 1 9 31 75 92 90 0 1 9 45 126 246 272 211 0 1 12 60 223 501 839 823 558
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
Crossrefs
Programs
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PARI
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} K(q, t, k)={prod(j=1, #q, my(g=gcd(t, q[j]), e=(q[j]/g)); (1 - y^e + y^e/(1 - x^e) + O(x*x^k))^g) - 1} G(n)={my(s=0); forpart(q=n, s+=permcount(q)*exp(sum(t=1, n, substvec(K(q, t, n\t)/t, [x,y], [x^t,y^t])) + O(x*x^n))); s/n!} T(n)=[Vecrev(p) | p<-Vec(G(n))] { my(A=T(10)); for(i=1, #A, print(A[i])) } \\ Andrew Howroyd, Jan 16 2024
Extensions
Offset corrected by Andrew Howroyd, Jan 16 2024