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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jul 22 2015
STATUS
approved

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Last modified March 4 02:53 EST 2024. Contains 370522 sequences. (Running on oeis4.)