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A125026 Triangle read by rows: T(n,k) = k*binomial(n,k) + binomial(n-1,k) (1 <= k <= n).

%I A125026 #14 Nov 09 2019 01:11:34
%S A125026 1,3,2,5,7,3,7,15,13,4,9,26,34,21,5,11,40,70,65,31,6,13,57,125,155,
%T A125026 111,43,7,15,77,203,315,301,175,57,8,17,100,308,574,686,532,260,73,9,
%U A125026 19,126,444,966,1386,1344,876,369,91,10,21,155,615,1530,2562,2982,2430,1365
%N A125026 Triangle read by rows: T(n,k) = k*binomial(n,k) + binomial(n-1,k) (1 <= k <= n).
%C A125026 Also A007318 * A127899 (unsigned) as a product of two infinite lower triangular matrices. - _Gary W. Adamson_, Feb 19 2007
%e A125026 First few rows of the triangle are
%e A125026    1;
%e A125026    3,   2;
%e A125026    5,   7,   3;
%e A125026    7,  15,  13,   4;
%e A125026    9,  26,  34,  21,   5;
%e A125026   11,  40,  70,  65,  31,   6;
%e A125026   13,  57, 125, 155, 111,  43,  7;
%e A125026   ...
%p A125026 T:=(n,k)->k*binomial(n,k)+binomial(n-1,k): for n from 1 to 12 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form
%Y A125026 Cf. A099035 (row sums).
%K A125026 nonn,tabl
%O A125026 1,2
%A A125026 _Gary W. Adamson_, Nov 15 2006
%E A125026 Edited by _N. J. A. Sloane_, Nov 29 2006