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A130301 Triangle read by rows: A130296 * A007318, as infinite lower triangular matrices.

%I A130301 #25 May 29 2023 11:29:37
%S A130301 1,3,1,5,3,1,7,6,4,1,9,10,10,5,1,11,15,20,15,6,1,13,21,35,35,21,7,1,
%T A130301 15,28,56,70,56,28,8,1,17,36,84,126,126,84,36,9,1,19,45,120,210,252,
%U A130301 210,120,45,10,1,21,55,165,330,462,462,330,165,55,11,1
%N A130301 Triangle read by rows: A130296 * A007318, as infinite lower triangular matrices.
%C A130301 Row sums = A083706: (1, 4, 9, 18, 35, 68, ...).
%C A130301 A130300 = A007318 * A130296.
%C A130301 The lower triangular matrix A130296 is equal to the restriction of the square array A051340 to its lower left triangular part. So this is also equal to (A051340) * A007318, where (A051340) is the lower triangular part of A051340, i.e., A051340[i,j] replaced by zero for j > i: see  Mathar's Maple code. - _M. F. Hasler_, Aug 15 2015
%F A130301 A130301[m,n] = A121775[m,n] for n >= m/2. A130301[m,1] = 2m-1, A130301[m,2] = A000217[m-1], A130301[m,m] = 1, A130301[m,m-1] = m for m>2. - _M. F. Hasler_, Aug 15 2015
%e A130301 First few rows of the triangle:
%e A130301    1;
%e A130301    3,  1;
%e A130301    5,  3,  1;
%e A130301    7,  6,  4,  1;
%e A130301    9, 10, 10,  5,  1;
%e A130301   11, 15, 20, 15,  6,  1;
%e A130301   13, 21, 35, 35, 21,  7,  1;
%e A130301   ...
%p A130301 A130301 := proc(n, k)
%p A130301     add( A051340(n, i)*binomial(i, k), i=k..n);
%p A130301 end proc: # _R. J. Mathar_, Jul 16 2015
%Y A130301 Cf. A083706, A130296, A130300.
%K A130301 nonn,tabl
%O A130301 1,2
%A A130301 _Gary W. Adamson_, May 20 2007
%E A130301 Corrected (missing a(15)=1 inserted) by _M. F. Hasler_, Aug 15 2015
%E A130301 a(26) = 27 corrected and more terms from _Georg Fischer_, May 29 2023