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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. 5
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..53.

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}]

CROSSREFS

Row sums are A322555.

Cf. A000569, A005176, A058891, A059441, A295193, A301481, A306017, A306019, A306021, A319169, A319190, A319612.

Sequence in context: A294950 A294609 A204180 * A106340 A156610 A203460

Adjacent sequences:  A319726 A319727 A319728 * A319730 A319731 A319732

KEYWORD

nonn,tabl

AUTHOR

Gus Wiseman, Dec 17 2018

STATUS

approved

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Last modified April 3 03:42 EDT 2020. Contains 333195 sequences. (Running on oeis4.)