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A289710
Triangle T(n,r) read by rows: order of the semigroup of orientation-preserving partial transformations of n elements with breath r.
2
1, 1, 1, 1, 4, 4, 1, 9, 27, 24, 1, 16, 96, 208, 128, 1, 25, 250, 950, 1325, 610, 1, 36, 540, 3120, 7290, 7416, 2742, 1, 49, 1029, 8330, 28665, 47922, 38563, 11970, 1, 64, 1792, 19264, 90720, 219968, 287168, 191808, 51424, 1, 81, 2916, 40068, 246078, 806274, 1509732, 1619676, 926073, 218718
OFFSET
0,5
EXAMPLE
1 ;
1 1;
1 4 4;
1 9 27 24;
1 16 96 208 128;
1 25 250 950 1325 610;
1 36 540 3120 7290 7416 2742;
1 49 1029 8330 28665 47922 38563 11970;
1 64 1792 19264 90720 219968 287168 191808 51424;
1 81 2916 40068 246078 806274 1509732 1619676 926073 218718;
MAPLE
A289710 := proc(n, r)
if r = 0 then
1;
else
r*binomial(n, r)*binomial(n+r-1, n-1)-n*(r-1)*binomial(n, r) ;
end if ;
end proc:
CROSSREFS
Cf. A092364 (column r=2), A289713 (row sums)
Sequence in context: A080721 A123588 A373504 * A243594 A360707 A365674
KEYWORD
tabl,nonn,easy
AUTHOR
R. J. Mathar, Sep 02 2017
STATUS
approved