A335362 Triangle T(n,d) read by rows: the number of mixed trees with n>=1 nodes and 0<=d<n arcs.

1, 1, 1, 1, 2, 3, 2, 5, 10, 8, 3, 12, 32, 40, 27, 6, 30, 99, 178, 187, 91, 11, 74, 298, 692, 1019, 854, 350, 23, 188, 890, 2538, 4751, 5692, 4074, 1376, 47, 478, 2627, 8886, 20260, 31188, 31856, 19602, 5743, 106, 1235, 7734, 30270, 81170, 152509, 200413, 177266, 96035, 24635

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows).

R. J. Mathar, Mixed Trees A335362

Index entries for sequences related to trees

Example

The triangle starts
1;
1, 1;
1, 2, 3;
2, 5,10, 8;
3,12,32,40,27;
There are T(3,1)=2 mixed trees on 3 nodes with one directed edge (the edge can point towards the middle node or away from it).

Prog

(PARI) \\ Here R(n) is rooted mixed trees as g.f.
EulerMTS(p)={my(n=serprec(p, x)-1, vars=variables(p)); exp(sum(i=1, n, substvec(p + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i))}
R(n) = {my(p=x+O(x^2)); for(n=2, n, p=x*EulerMTS(2*y*p + p)); p}
T(n) = {my(p=R(n)); [Vecrev(p) | p<-Vec(p + (subst(subst(p + O(x*x^(n\2)), x, x^2), y, y^2) - (2*y+1)*p^2)/2)]}
{ my(A=T(10)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Mar 23 2023

Crossrefs

Cf. A000055 (column d=0), A000238 (diagonal d=n-1), A000106 (column d=1), A006965 (row sums), A335601 (subdiagonal d=n-2).

Sequence in context: A296662 A353299 A349790 * A371395 A059098 A082050

Adjacent sequences: A335359 A335360 A335361 * A335363 A335364 A335365

Keyword

nonn,tabl

Author

R. J. Mathar, Jun 03 2020

Extensions

Completed row n=9. - R. J. Mathar, Jun 11 2020

Terms a(46) and beyond from Andrew Howroyd, Mar 23 2023

Status

approved