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A092393 Triangle read by rows: T(n,k) = (n+k)*binomial(n,k) (for k=0..n-1).

%I A092393 #26 Nov 02 2023 20:10:58
%S A092393 1,2,6,3,12,15,4,20,36,28,5,30,70,80,45,6,42,120,180,150,66,7,56,189,
%T A092393 350,385,252,91,8,72,280,616,840,728,392,120,9,90,396,1008,1638,1764,
%U A092393 1260,576,153,10,110,540,1560,2940,3780,3360,2040,810,190,11,132,715
%N A092393 Triangle read by rows: T(n,k) = (n+k)*binomial(n,k) (for k=0..n-1).
%H A092393 Paolo Xausa, <a href="/A092393/b092393.txt">Table of n, a(n) for n = 1..11325</a> (rows 1..150 of the triangle, flattened)
%F A092393 First column = positive integers;
%F A092393 second column = A002378;
%F A092393 third column = A077414;
%F A092393 main diagonal (i.e., T(n,n) = (n+n)*binomial(n,n) = 2n, which is not included in this sequence) = even integers;
%F A092393 second diagonal = A000384.
%F A092393 Row sums = 1, 8, 30, 88, 230,... = A167667(n)-2n. - _R. J. Mathar_, Nov 02 2023
%e A092393 Triangle starts:
%e A092393 1;
%e A092393 2, 6;
%e A092393 3, 12, 15;
%e A092393 4, 20, 36,  28;
%e A092393 5, 30, 70,  80,  45;
%e A092393 6, 42, 120, 180, 150, 66;
%e A092393 ...
%p A092393 A092393 := proc(n,k)
%p A092393     (n+k)*binomial(n,k) ;
%p A092393 end proc:
%p A092393 seq(seq( A092393(n,k),k=0..n-1),n=1..12) ; # _R. J. Mathar_, Nov 02 2023
%t A092393 A092393row[n_]:=Table[(n+k)Binomial[n,k],{k,0,n-1}];Array[A092393row,10]  (* _Paolo Xausa_, Nov 02 2023 *)
%o A092393 (PARI) T(n,k)=binomial(n,k)*(n+k)
%Y A092393 Cf. A029635.
%K A092393 nonn,tabl
%O A092393 1,2
%A A092393 _Benoit Cloitre_, Mar 21 2004