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 A329228 Triangle read by rows: T(n,k) is the number of digraphs on n unlabeled vertices such that every vertex has outdegree k, n >= 1, 0 <= k < n. 9
 1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 13, 79, 13, 1, 1, 40, 1499, 1499, 40, 1, 1, 100, 35317, 257290, 35317, 100, 1, 1, 291, 967255, 56150820, 56150820, 967255, 291, 1, 1, 797, 29949217, 14971125930, 111359017198, 14971125930, 29949217, 797, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 EXAMPLE Triangle begins: 1; 1, 1; 1, 2, 1; 1, 6, 6, 1; 1, 13, 79, 13, 1; 1, 40, 1499, 1499, 40, 1; 1, 100, 35317, 257290, 35317, 100, 1; 1, 291, 967255, 56150820, 56150820, 967255, 291, 1; ... PROG (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} E(v, x) = {my(r=1/(1-x)); for(i=1, #v, r=serconvol(r, prod(j=1, #v, my(g=gcd(v[i], v[j])); (1 + x^(v[j]/g))^g)/(1 + x))); r} Row(n)={my(s=0); forpart(p=n, s+=permcount(p)*E(p, x+O(x^n))); Vec(s/n!)} { for(n=1, 8, print(Row(n))) } CROSSREFS Columns k=0..5 are A000012, A001373, A129524, A185193, A185194, A185303. Row sums are A329234. Sequence in context: A145903 A223257 A173881 * A172373 A174411 A322620 Adjacent sequences: A329225 A329226 A329227 * A329229 A329230 A329231 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Nov 08 2019 STATUS approved

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Last modified May 30 13:54 EDT 2023. Contains 363050 sequences. (Running on oeis4.)