OFFSET
1,9
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1154 (rows 1..200)
EXAMPLE
Triangle begins:
1
1
1
1 1
1 1
1 3
1 3
1 6 1
1 7 1
1 11 4
1 13 6
1 20 16
1 23 23
1 33 46
1 40 70
The T(11,3) = 6 rooted trees:
(((oo)(oo))((oo)(ooooo)))
(((oo)(oo))((ooo)(oooo)))
(((oo)(ooo))((oo)(oooo)))
(((oo)(ooo))((ooo)(ooo)))
(((oo)(oo))((oo)(oo)(ooo)))
(((oo)(ooo))((oo)(oo)(oo)))
MATHEMATICA
qurt[n_]:=If[n==1, {{}}, Join@@Table[Union[Sort/@Tuples[qurt/@ptn]], {ptn, Select[IntegerPartitions[n], Length[#]>1&]}]];
DeleteCases[Table[Length[Select[qurt[n], SameQ[##, k]&@@Length/@Position[#, {}]&]], {n, 10}, {k, 0, n-1}], 0, {2}]
PROG
(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
T(n)={my(u=vector(n), v=vector(n), h=1); u[1]=1; while(u, v+=u*h; h*=x; u=EulerT(u)-u); v[1]=x; [Vecrev(p/x) | p<-v]}
{ my(A=T(15)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Dec 09 2020
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Oct 07 2018
EXTENSIONS
Terms a(36) and beyond from Andrew Howroyd, Dec 09 2020
Name clarified by Andrew Howroyd, Dec 09 2020
STATUS
approved