OFFSET
0,5
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1274
EXAMPLE
Triangle begins:
1
1 1
0 2 3
0 1 10 16
0 0 12 79 125
0 0 6 162 847 1296
0 0 1 179 2565 11436 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[Subsets[multsubs[Range[k], 2], {n}], And[Union@@#==Range[k], Length[csm[#]]==1]&]]], {n, 0, 6}, {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 + 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
Column sums are A062740.
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Nov 28 2018
EXTENSIONS
Terms a(28) and beyond from Andrew Howroyd, Nov 29 2018
STATUS
approved