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A296419
Triangle T(i,j) read by rows: Number of plane bipolar orientations with i+1 vertices and j+1 faces.
3
1, 1, 4, 1, 10, 50, 1, 20, 175, 980, 1, 35, 490, 4116, 24696, 1, 56, 1176, 14112, 116424, 731808, 1, 84, 2520, 41580, 457380, 3737448, 24293412, 1, 120, 4950, 108900, 1557270, 16195608, 131589315, 877262100, 1, 165, 9075, 259545, 4723719, 61408347, 614083470, 4971151900, 33803832920
OFFSET
1,3
LINKS
E. Fusy, D. Poulalhon, and G. Schaeffer, Bijective counting of plane bipolar orientations, El. Notes Discr. Math. 29 (2007) 283-287.
FORMULA
T(i,j) = T(j,i) = 2*(i+j-2)!*(i+j-1)!*(i+j)!/((i-1)!*i!*(i+1)!*(j-1)!*j!*(j+1)!).
EXAMPLE
The triangle starts in row 1 as
1;
1, 4;
1, 10, 50;
1, 20, 175, 980;
1, 35, 490, 4116, 24696;
1, 56, 1176, 14112, 116424, 731808;
1, 84, 2520, 41580, 457380, 3737448, 24293412;
1, 120, 4950, 108900, 1557270, 16195608, 131589315, 877262100;
MAPLE
A296419 := proc(i, j)
2*(i+j-2)!*(i+j-1)!*(i+j)!/(i-1)!/i!/(i+1)!/(j-1)!/j!/(j+1)! ;
end proc:
seq(seq(A296419(i, j), j=1..i), i=1..10) ;
CROSSREFS
Cf. rows/columns: A006542, A047819, A107915, A140901, A140903, A140907.
Sequence in context: A307529 A019213 A019128 * A301390 A283433 A121463
KEYWORD
nonn,tabl,easy
AUTHOR
R. J. Mathar, Feb 25 2018
STATUS
approved