%I #20 Jan 07 2024 16:27:00

%S 1,2,3,3,8,5,4,15,18,7,5,24,42,32,9,6,35,80,90,50,11,7,48,135,200,165,

%T 72,13,8,63,210,385,420,273,98,15,9,80,308,672,910,784,420,128,17,10,

%U 99,432,1092,1764,1890,1344,612,162,19,11,120,585,1680,3150,4032,3570,2160,855,200,21

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

%H Andrew Howroyd, <a href="/A347823/b347823.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)

%F T(n,k) = A094727(n+1,k)*A007318(n,k).

%F Row g.f.: (1 + x)^(n-1)*(1 + n + x + 2*n*x). - _Stefano Spezia_, Jan 23 2022

%e Triangle begins:

%e 1;

%e 2, 3;

%e 3, 8, 5;

%e 4, 15, 18, 7;

%e 5, 24, 42, 32, 9;

%e 6, 35, 80, 90, 50, 11;

%e 7, 48, 135, 200, 165, 72, 13;

%e 8, 63, 210, 385, 420, 273, 98, 15;

%e ...

%o (PARI) T(n,k) = (n+k+1)*binomial(n,k) \\ _Andrew Howroyd_, Jan 23 2022

%Y Row sums give A053220.

%Y Columns give A000027, A005563, A212343.

%Y Diagonals give A005408, A001105, A059270, A112742.

%Y Cf. A007318, A094727.

%K nonn,tabl

%O 0,2

%A _Jules Beauchamp_, Jan 23 2022