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