A124727 - OEIS

%I #9 Nov 21 2013 12:49:01

%S 1,2,2,3,5,3,4,9,10,4,5,14,22,17,5,6,20,40,45,26,6,7,27,65,95,81,37,7,

%T 8,35,98,175,196,133,50,8,9,44,140,294,406,364,204,65,9,10,54,192,462,

%U 756,840,624,297,82,10,11,65,255,690,1302,1722,1590,1005,415,101,11,12,77

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

%C Triangle is P*M, where P is Pascal's triangle as an infinite lower triangular matrix and M is the infinite bidiagonal matrix with (1,2,3...) in the main diagonal and (1,1,1...) in the subdiagonal.

%e First few rows of the triangle are:

%e 1;

%e 2, 2;

%e 3, 5, 3;

%e 4, 9, 10, 4;

%e 5, 14, 22, 17, 5;

%e 6, 20, 40, 45, 26, 6

%e ...

%p T:=(n,k)->k*binomial(n-1,k-1)+binomial(n-1,k): for n from 1 to 12 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form

%t Flatten[Table[k Binomial[n-1,k-1]+Binomial[n-1,k],{n,20},{k,n}]] (* _Harvey P. Dale_, Jan 28 2012 *)

%Y Row sums = A047859: (1, 4, 11, 27, 143, 319...) A124726 is generated in an analogous manner by taking M*P instead of P*M.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_ & _Roger L. Bagula_, Nov 05 2006

%E Edited by _N. J. A. Sloane_, Nov 24 2006