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A322148
Regular triangle where T(n,k) is the number of labeled connected multigraphs with loops with n edges and k vertices.
3
1, 1, 1, 1, 3, 3, 1, 6, 16, 16, 1, 10, 51, 127, 125, 1, 15, 126, 574, 1347, 1296, 1, 21, 266, 1939, 8050, 17916, 16807, 1, 28, 504, 5440, 35210, 135156, 286786, 262144, 1, 36, 882, 13387, 125730, 736401, 2642122, 5368728, 4782969, 1, 45, 1452, 29854, 388190, 3239491, 17424610, 58925728, 115089813, 100000000
OFFSET
0,5
EXAMPLE
Triangle begins:
1
1 1
1 3 3
1 6 16 16
1 10 51 127 125
1 15 126 574 1347 1296
1 21 266 1939 8050 17916 16807
MATHEMATICA
multsubs[set_, k_]:=If[k==0, {{}}, Join@@Table[Prepend[#, set[[i]]]&/@multsubs[Drop[set, i-1], k-1], {i, Length[set]}]];
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Union[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];
Table[If[n==0, 1, Length[Select[multsubs[multsubs[Range[k], 2], n], And[Union@@#==Range[k], Length[csm[#]]==1]&]]], {n, 0, 5}, {k, 1, n+1}]
PROG
(PARI)
Connected(v)={my(u=vector(#v)); for(n=1, #u, u[n]=v[n] - sum(k=1, n-1, binomial(n-1, k)*v[k]*u[n-k])); u}
M(n)={Mat([Col(p, -(n+1)) | p<-Connected(vector(2*n, j, 1/(1 - x + O(x*x^n) )^binomial(j+1, 2)))[1..n+1]])}
{ my(T=M(10)); for(n=1, #T, print(T[n, ][1..n])) } \\ Andrew Howroyd, Nov 29 2018
CROSSREFS
Row sums are A322152. Last column is A000272.
Sequence in context: A117279 A234251 A049323 * A084144 A306759 A214362
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Nov 28 2018
EXTENSIONS
Offset corrected and terms a(28) and beyond from Andrew Howroyd, Nov 29 2018
STATUS
approved

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Last modified September 20 18:47 EDT 2024. Contains 376075 sequences. (Running on oeis4.)