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A260039
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Triangle read by rows giving numbers B(n,k) arising in the enumeration of doubly rooted tree maps.
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6
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1, 8, 2, 72, 30, 3, 720, 380, 72, 4, 7780, 4690, 1245, 140, 5, 89040, 58254, 19152, 3192, 240, 6, 1064644, 734496, 279972, 60648, 7000, 378, 7, 13173216, 9416688, 3997584, 1046832, 162000, 13752, 560, 8, 167522976, 122687334, 56488950, 17086608, 3285990, 382140, 24885, 792, 9
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OFFSET
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1,2
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COMMENTS
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See Mullin (1967) for precise definition.
What is the sequence 1, 8, 72, 720, 7780, 89040, 1064644, 13173216, 167522976, 2178520080, ... in the leading diagonal?
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LINKS
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FORMULA
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T(n,k) = (k+1)*A260040(n,k), n>=1, 0<=k<n.
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EXAMPLE
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Triangle begins:
1;
8, 2;
72, 30, 3;
720, 380, 72, 4;
...
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MAPLE
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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") ;
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MATHEMATICA
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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];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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