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A319729
Regular triangle read by rows where T(n,k) is the number of labeled simple graphs on n vertices where all non-isolated vertices have degree k.
6
1, 1, 1, 1, 3, 1, 1, 9, 7, 1, 1, 25, 37, 5, 1, 1, 75, 207, 85, 21, 1, 1, 231, 1347, 525, 591, 7, 1, 1, 763, 10125, 21385, 23551, 3535, 113, 1, 1, 2619, 86173, 180201, 1216701, 31647, 30997, 9, 1, 1, 9495, 819133, 12066705, 77636583, 66620631, 11485825, 286929, 955, 1
OFFSET
1,5
LINKS
FORMULA
T(n,k) = Sum_{i=1..n} binomial(n,i)*A059441(i,k) for k > 0. - Andrew Howroyd, Dec 26 2020
EXAMPLE
Triangle begins:
1
1 1
1 3 1
1 9 7 1
1 25 37 5 1
1 75 207 85 21 1
1 231 1347 525 591 7 1
1 763 10125 21385 23551 3535 113 1
1 2619 86173 180201 1216701 31647 30997 9 1
MATHEMATICA
Table[If[k==0, 1, Sum[Binomial[n, sup]*SeriesCoefficient[Product[1+Times@@x/@s, {s, Subsets[Range[sup], {2}]}], Sequence@@Table[{x[i], 0, k}, {i, sup}]], {sup, n}]], {n, 8}, {k, 0, n-1}]
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Dec 17 2018
STATUS
approved