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A110180 Triangle of generalized central trinomial coefficients. 4

%I

%S 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,

%T 161,91,25,11,1,1,1,393,581,331,145,31,13,1,1,1,1107,2045,1441,561,

%U 211,37,15,1,1,1,3139,7393,5797,2841,851,289,43,17,1,1

%N Triangle of generalized central trinomial coefficients.

%C Rows sums are A110181. Diagonal sums are A110182. Columns include central trinomial coefficients A002426, A084601, A084603, A084605, A098264. T(n,k) = central coefficient (1 + x + kx^2)^n.

%H G. C. Greubel, <a href="/A110180/b110180.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%F Number triangle T(n, k) = Sum_{j=0..floor((n-k)/2)} C(n-k, j)*C(n-k-j, j)*k^j.

%e Rows begin

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 3, 1, 1;

%e 1, 7, 5, 1, 1;

%e 1, 19, 13, 7, 1, 1;

%t 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 *)

%K easy,nonn,tabl

%O 0,8

%A _Paul Barry_, Jul 14 2005

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Last modified June 17 17:39 EDT 2021. Contains 345085 sequences. (Running on oeis4.)