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A241188
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Triangle T(n,s) of Dynkin type D_n read by rows (n >= 2, 0 <= s <= n).
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0
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1, 2, 1, 1, 3, 5, 5, 1, 4, 9, 16, 20, 1, 5, 14, 30, 55, 77, 1, 6, 20, 50, 105, 196, 294, 1, 7, 27, 77, 182, 378, 714, 1122, 1, 8, 35, 112, 294, 672, 1386, 2640, 4290, 1, 9, 44, 156, 450, 1122, 2508, 5148, 9867, 16445
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OFFSET
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2,2
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LINKS
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FORMULA
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T(n,s) = [n+s-2,s] for 0 <= s < n, T(n,n) = [2n-2,n-2], where [t,s] stands for binomial(t,s)*(s+t)/t.
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EXAMPLE
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Triangle begins:
1, 2, 1,
1, 3, 5, 5,
1, 4, 9, 16, 20,
1, 5, 14, 30, 55, 77,
1, 6, 20, 50, 105, 196, 294,
1, 7, 27, 77, 182, 378, 714, 1122,
1, 8, 35, 112, 294, 672, 1386, 2640, 4290,
1, 9, 44, 156, 450, 1122, 2508, 5148, 9867, 16445,
...
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MATHEMATICA
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f[t_, s_] := Binomial[t, s] (s + t)/t;
T[_, 0] = 1; T[n_, n_] := f[2 n - 2, n - 2]; T[n_, s_] := f[n + s - 2, s];
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CROSSREFS
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See A009766 for the case of type A.
See A059481 for the case of type B/C.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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