A110180 Triangle of generalized central trinomial coefficients.
1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 7, 5, 1, 1, 1, 19, 13, 7, 1, 1, 1, 51, 49, 19, 9, 1, 1, 1, 141, 161, 91, 25, 11, 1, 1, 1, 393, 581, 331, 145, 31, 13, 1, 1, 1, 1107, 2045, 1441, 561, 211, 37, 15, 1, 1, 1, 3139, 7393, 5797, 2841, 851, 289, 43, 17, 1, 1
Offset: 0
Examples
Rows begin 1; 1, 1; 1, 1, 1; 1, 3, 1, 1; 1, 7, 5, 1, 1; 1, 19, 13, 7, 1, 1;
Links
- G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Programs
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Mathematica
T[n_, 0] := 1; T[n_, k_] := Sum[Binomial[n - k, j]*Binomial[n - k - j, j]*k^j, {j, 0, Floor[(n - k)/2]}]; Table[T[n, k], {n, 0, 49}, {k, 0, n}] // Flatten (* G. C. Greubel, Mar 05 2017 *)
Formula
Number triangle T(n, k) = Sum_{j=0..floor((n-k)/2)} C(n-k, j)*C(n-k-j, j)*k^j.
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