OFFSET
1,2
COMMENTS
See Mullin (1967) for precise definition.
What is the sequence 1, 8, 72, 720, 7780, 89040, 1064644, 13173216, 167522976, 2178520080, ... in the leading diagonal?
LINKS
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] [DOI]
FORMULA
T(n,k) = (k+1)*A260040(n,k), n>=1, 0<=k<n.
Conjecture: T(n,0) = n*A168452(n-1). - R. J. Mathar, Jul 22 2015
EXAMPLE
Triangle begins:
1;
8, 2;
72, 30, 3;
720, 380, 72, 4;
...
MAPLE
bEq64 := proc(k, u)
(k+1)*(2*u+k)!*(2*u+k+2)!/u!/(u+k+2)!/(u+k+1)!/(u+1)! ;
end proc:
Eq65 := proc(n, k)
add( bEq64(k, u)*bEq64(k, n-k-1-u), u=0..n-k-1) ;
end proc:
B := proc(n, k)
n*Eq65(n, k) ;
end proc:
for n from 1 to 10 do
for k from 0 to n-1 do
printf("%a, ", B(n, k)) ;
end do:
printf("\n") ;
end do: # R. J. Mathar, Jul 22 2015
MATHEMATICA
bEq64 [k_, u_] := (k + 1)*(2u + k)!*(2u + k + 2)!/u!/(u + k + 2)!/(u + k + 1)!/(u + 1)!;
Eq65[n_, k_] := Sum[bEq64[k, u]*bEq64[k, n - k - 1 - u], {u, 0, n - k - 1}];
B[n_, k_] := n*Eq65[n, k];
Table[B[n, k], {n, 1, 10}, {k, 0, n - 1}] // Flatten (* Jean-François Alcover, May 08 2023, after R. J. Mathar *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jul 22 2015
STATUS
approved