A309936 Irregular triangle read by rows: T(n,k) is the number of unlabeled loopless multigraphs with n edges covering k vertices, n >= 1, 1 <= k <= 2*n.
0, 1, 0, 1, 1, 1, 0, 1, 2, 3, 1, 1, 0, 1, 3, 7, 6, 4, 1, 1, 0, 1, 4, 13, 17, 17, 8, 4, 1, 1, 0, 1, 6, 25, 44, 56, 41, 24, 9, 4, 1, 1, 0, 1, 7, 40, 101, 164, 158, 117, 57, 26, 9, 4, 1, 1, 0, 1, 9, 65, 216, 450, 562, 503, 315, 162, 64, 27, 9, 4, 1, 1
Offset: 1
Examples
Triangle begins: 0, 1; 0, 1, 1, 1; 0, 1, 2, 3, 1, 1; 0, 1, 3, 7, 6, 4, 1, 1; 0, 1, 4, 13, 17, 17, 8, 4, 1, 1; 0, 1, 6, 25, 44, 56, 41, 24, 9, 4, 1, 1; 0, 1, 7, 40, 101, 164, 158, 117, 57, 26, 9, 4, 1, 1; ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..650 (rows 1..25)
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} edges(v, t) = {prod(i=2, #v, prod(j=1, i-1, my(g=gcd(v[i], v[j])); t(v[i]*v[j]/g)^g )) * prod(i=1, #v, my(c=v[i]); t(c)^((c-1)\2)*if(c%2, 1, t(c/2)))} C(n,m)={my(s=O(x*x^m)); forpart(p=n, s+=permcount(p)/edges(p, i->1-x^i+O(x*x^m))); Col(s/n!)} T(m) = {my(n=2*m, A=Mat(vector(n+1, n, C(n-1,m)))); A[2..m+1, 2..n+1]-A[2..m+1, 1..n]} { my(A=T(8)); for(n=1, matsize(A)[1], print(A[n, 1..2*n])) }
Comments