A143185 - OEIS

%I #8 Apr 24 2024 03:06:11

%S 1,1,1,1,2,1,1,6,6,1,1,12,6,12,1,1,20,20,20,20,1,1,30,45,20,45,30,1,1,

%T 42,84,70,70,84,42,1,1,56,140,168,70,168,140,56,1,1,72,216,336,252,

%U 252,336,216,72,1,1,90,315,600,630,252,630,600,315,90,1

%N Triangle read by rows: T(n, k) = (1 + abs(n-2*k))*binomial(n,k), with T(n, 0) = T(n, n) = 1.

%H G. C. Greubel, <a href="/A143185/b143185.txt">Rows n = 0..50 of the triangle, flattened</a>

%F T(n, k) = (1 + abs(n-2*k))*binomial(n,k) for 1 <= k <= n-1, with T(n, 0) = T(n, n) = 1.

%F T(n, n-k) = T(n, k).

%e Table begins as:

%e   1;

%e   1,  1;

%e   1,  2,   1;

%e   1,  6,   6,   1;

%e   1, 12,   6,  12,   1;

%e   1, 20,  20,  20,  20,   1;

%e   1, 30,  45,  20,  45,  30,   1;

%e   1, 42,  84,  70,  70,  84,  42,   1;

%e   1, 56, 140, 168,  70, 168, 140,  56,   1;

%e   1, 72, 216, 336, 252, 252, 336, 216,  72,  1;

%e   1, 90, 315, 600, 630, 252, 630, 600, 315, 90, 1;

%t T[n_, k_] = If[k*(n-k)==0, 1, (1 + Abs[n-2*k])*Binomial[n,k]];

%t Table[T[n,k], {n,0,12}, {k,0,n}]//Flatten

%o (Magma)

%o A143185:= func< n,k | k eq 0 or k eq n select 1 else (1+Abs(n-2*k))*Binomial(n,k) >;

%o [A143185(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Apr 23 2024

%o (SageMath)

%o def A143185(n,k): return 1 if (k==0 or k==n) else (1+abs(n-2*k))*binomial(n ,k)

%o flatten([[A143185(n,k) for k in range(n+1)] for n in range(13)]) # _G. C. Greubel_, Apr 23 2024

%K nonn,tabl

%O 0,5

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 17 2008

%E Edited by _G. C. Greubel_, Apr 23 2024