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A124732 Triangle P*M, where P is the Pascal triangle written as an infinite lower triangular matrix and M is the infinite bidiagonal matrix with (1,2,1,2,...) in the main diagonal and (2,1,2,1,...) in the subdiagonal.

%I A124732 #9 Jul 21 2019 21:58:00
%S A124732 1,3,2,5,5,1,7,9,5,2,9,14,14,9,1,11,20,30,25,7,2,13,27,55,55,27,13,1,
%T A124732 15,35,91,105,77,49,9,2,17,44,140,182,182,140,44,17,1,19,54,204,294,
%U A124732 378,336,156,81,11,2,21,65,285,450,714,714,450,285,65,21,1,23,77,385,660
%N A124732 Triangle P*M, where P is the Pascal triangle written as an infinite lower triangular matrix and M is the infinite bidiagonal matrix with (1,2,1,2,...) in the main diagonal and (2,1,2,1,...) in the subdiagonal.
%C A124732 Row sums = A052940: (1, 5, 11, 23, 47, 95, ...).
%F A124732 T(n,k) = binomial(n,k)*(3n-(-1)^k*(n-2*k))/(2n) (1 <= k <= n).
%e A124732 First 3 rows of the triangle are (1; 3,2; 5,5,1) since [1,0,0; 1,1,0; 1,2,1] * [1,0,0; 2,2,0; 0,1,1] = [1,0,0; 3,2,0; 5,5,1].
%e A124732 First few rows of the triangle are:
%e A124732    1;
%e A124732    3,   2;
%e A124732    5,   5,   1;
%e A124732    7,   9,   5,   2;
%e A124732    9,  14,  14,   9,   1;
%e A124732   11,  20,  30,  25,   7,   2;
%e A124732   13,  27,  55,  55,  27,  13,   1;
%e A124732   15,  35,  91, 105,  77,  49,   9,   2;
%e A124732   ...
%p A124732 T:=(n,k)->binomial(n,k)*(3*n-(-1)^k*(n-2*k))/2/n: for n from 1 to 12 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form
%Y A124732 Cf. A124730, A052940.
%K A124732 nonn,tabl
%O A124732 1,2
%A A124732 _Gary W. Adamson_ & _Roger L. Bagula_, Nov 05 2006
%E A124732 Edited by _N. J. A. Sloane_, Nov 24 2006