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A347823 Triangle read by rows: T(n,k) = (n+k+1)*binomial(n,k), 0 <= k <= n.

%I A347823 #20 Jan 07 2024 16:27:00
%S A347823 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 A347823 72,13,8,63,210,385,420,273,98,15,9,80,308,672,910,784,420,128,17,10,
%U A347823 99,432,1092,1764,1890,1344,612,162,19,11,120,585,1680,3150,4032,3570,2160,855,200,21
%N A347823 Triangle read by rows: T(n,k) = (n+k+1)*binomial(n,k), 0 <= k <= n.
%H A347823 Andrew Howroyd, <a href="/A347823/b347823.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)
%F A347823 T(n,k) = A094727(n+1,k)*A007318(n,k).
%F A347823 Row g.f.: (1 + x)^(n-1)*(1 + n + x + 2*n*x). - _Stefano Spezia_, Jan 23 2022
%e A347823 Triangle begins:
%e A347823   1;
%e A347823   2,  3;
%e A347823   3,  8,   5;
%e A347823   4, 15,  18,   7;
%e A347823   5, 24,  42,  32,   9;
%e A347823   6, 35,  80,  90,  50,  11;
%e A347823   7, 48, 135, 200, 165,  72, 13;
%e A347823   8, 63, 210, 385, 420, 273, 98, 15;
%e A347823   ...
%o A347823 (PARI) T(n,k) = (n+k+1)*binomial(n,k) \\ _Andrew Howroyd_, Jan 23 2022
%Y A347823 Row sums give A053220.
%Y A347823 Columns give A000027, A005563, A212343.
%Y A347823 Diagonals give A005408, A001105, A059270, A112742.
%Y A347823 Cf. A007318, A094727.
%K A347823 nonn,tabl
%O A347823 0,2
%A A347823 _Jules Beauchamp_, Jan 23 2022