A059441 Triangle T(n,k) (n >= 1, 0 <= k <= n-1) giving number of regular labeled graphs with n nodes and degree k, read by rows.
1, 1, 1, 1, 0, 1, 1, 3, 3, 1, 1, 0, 12, 0, 1, 1, 15, 70, 70, 15, 1, 1, 0, 465, 0, 465, 0, 1, 1, 105, 3507, 19355, 19355, 3507, 105, 1, 1, 0, 30016, 0, 1024380, 0, 30016, 0, 1, 1, 945, 286884, 11180820, 66462606, 66462606, 11180820, 286884, 945, 1
Offset: 1
Examples
1; 1, 1; 1, 0, 1; 1, 3, 3, 1; 1, 0, 12, 0, 1; 1, 15, 70, 70, 15, 1; 1, 0, 465, 0, 465, 0, 1; 1, 105, 3507, 19355, 19355, 3507, 105, 1; 1, 0, 30016, 0, 1024380, ...; 1, 945, 286884, 11180820, 66462606, ...; 1, 0, 3026655, 0, 5188453830, ...;
References
- L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 279.
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..300 (rows 1..24)
- Denis S. Krotov, [[2,10],[6,6]]-equitable partitions of the 12-cube, arXiv:2012.00038 [math.CO], 2020.
- Brendan D. McKay, Applications of a technique for labeled enumeration, Congress. Numerantium, 40 (1983), 207-221. See page 216.
- Wikipedia, Regular graph
Crossrefs
Programs
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Mathematica
Table[SeriesCoefficient[Product[1+Times@@x/@s,{s,Subsets[Range[n],{2}]}],Sequence@@Table[{x[i],0,k},{i,n}]],{n,9},{k,0,n-1}] (* Gus Wiseman, Dec 24 2018 *) -
PARI
for(n=1, 10, print(A059441(n))) \\ See A295193 for script, Andrew Howroyd, Aug 28 2019
Extensions
a(37)-a(55) from Andrew Howroyd, Aug 25 2017
Comments