OFFSET
1,5
FORMULA
Column k is the inverse Euler transform of column k of A301922. - Andrew Howroyd, Aug 26 2019
EXAMPLE
Triangle begins:
1
0 1
0 2 1
0 6 3 1
0 21 29 4 1
0 112 2101 150 5 1
0 853 7011181 7013164 1037 6 1
...
The T(4,2) = 6 hypergraphs:
{{1,3},{2,4},{3,4}}
{{1,4},{2,4},{3,4}}
{{1,2},{1,3},{2,4},{3,4}}
{{1,4},{2,3},{2,4},{3,4}}
{{1,3},{1,4},{2,3},{2,4},{3,4}}
{{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}
PROG
(PARI)
InvEulerT(v)={my(p=log(1+x*Ser(v))); dirdiv(vector(#v, n, polcoeff(p, n)), vector(#v, n, 1/n))}
permcount(v)={my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
rep(typ)={my(L=List(), k=0); for(i=1, #typ, k+=typ[i]; listput(L, k); while(#L<k, listput(L, #L))); Vec(L)}
can(v, f)={my(d=1, u=v); while(d>0, u=vecsort(apply(f, u)); d=lex(u, v)); !d}
Q(n, k, perm)={my(t=0); forsubset([n, k], v, t += can(Vec(v), t->perm[t])); t}
U(n, k)={my(s=0); forpart(p=n, s += permcount(p)*2^Q(n, k, rep(p))); s/n!}
A(n)={Mat(vector(n, k, InvEulerT(vector(n, i, U(i, k)-U(i-1, k)))~))}
{ my(T=A(8)); for(n=1, #T, print(T[n, 1..n])) } \\ Andrew Howroyd, Aug 26 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Jun 19 2018
EXTENSIONS
Terms a(16) and beyond from Andrew Howroyd, Aug 26 2019
STATUS
approved