A260040 Triangle read by rows giving numbers H(n,k), number of classes of twin-tree-rooted maps with n edges whose root bond contains k edges.

1, 8, 1, 72, 15, 1, 720, 190, 24, 1, 7780, 2345, 415, 35, 1, 89040, 29127, 6384, 798, 48, 1, 1064644, 367248, 93324, 15162, 1400, 63, 1, 13173216, 4708344, 1332528, 261708, 32400, 2292, 80, 1, 167522976, 61343667, 18829650, 4271652, 657198, 63690, 3555, 99, 1, 2178520080, 811147590, 265116720, 67358500, 12269312, 1506615, 117040, 5280, 120, 1

Offset

1,2

Comments

See Mullin (1967) for precise definition.

The sequence 1, 8, 72, 720,... in the first column has the same values as in A260039.

Links

Table of n, a(n) for n=1..55.

R. C. Mullin, On the average activity of a spanning tree of a rooted map, J. Combin. Theory, 3 (1967), 103-121.

R. C. Mullin, On the average activity of a spanning tree of a rooted map, J. Combin. Theory, 3 (1967), 103-121. [Annotated scanned copy]

Formula

(k+1)*T(n,k) = A260039(n,k), n>=1, 0<=k<n. [Mullin Eq. (7.1)]

Conjecture: T(n,n-2) = A005563(n) = 8, 15, 24,.... for n>=2. - R. J. Mathar, Jul 22 2015

Conjecture: T(n,n-3)= (n+1)*n*(5*n^2+7*n+6)/12 = 72, 190,.... for n>=3. - R. J. Mathar, Jul 22 2015

Example

Triangle begins:
1,
8,1,
72,15,1,
720,190,24,1,
...

Crossrefs

Row sums are A260041.

Sequence in context: A347489 A038279 A075503 * A051379 A143499 A114152

Adjacent sequences: A260037 A260038 A260039 * A260041 A260042 A260043

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jul 22 2015

Status

approved