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A135227 Triangle A000012 * A135225, read by rows.

%I A135227 #8 Mar 27 2022 19:03:26
%S A135227 1,2,1,3,2,1,4,3,3,1,5,4,6,4,1,6,5,10,10,5,1,7,6,15,20,15,6,1,8,7,21,
%T A135227 35,35,21,7,1,9,8,28,56,70,56,28,8,1,10,9,36,84,126,126,84,36,9,1,11,
%U A135227 10,45,120,210,252,210,120,45,10,1,12,11,55,165,330,462,462,330,165,55,11,1
%N A135227 Triangle A000012 * A135225, read by rows.
%C A135227 Row sums = A006127: (1, 3, 6, 11, 20, 37, ...).
%H A135227 G. C. Greubel, <a href="/A135227/b135227.txt">Rows n = 0..100 of triangle, flattened</a>
%F A135227 A000012 * A135225 as infinite lower triangular matrices. Left border of 1's in Pascal's Triangle (A007318) is replaced with a column of (1,2,3,...).
%F A135227 T(n,k) = binomial(n,k), with T(n,0) = n+1. - _G. C. Greubel_, Nov 20 2019
%e A135227 First few rows of the triangle:
%e A135227   1;
%e A135227   2, 1;
%e A135227   3, 2,  1;
%e A135227   4, 3,  3,  1;
%e A135227   5, 4,  6,  4,  1;
%e A135227   6, 5, 10, 10,  5, 1;
%e A135227   7, 6, 15, 20, 15, 6, 1;
%e A135227 ...
%p A135227 seq(seq( `if`(k=0, n+1, binomial(n,k)), k=0..n), n=0..12); # _G. C. Greubel_, Nov 20 2019
%t A135227 Table[If[k==0, n+1, Binomial[n, k]], {n, 0, 12}, {k, 0, n}]//Flatten (* _G. C. Greubel_, Nov 20 2019 *)
%o A135227 (PARI) T(n,k) = if(k==0, n+1, binomial(n,k)); \\ _G. C. Greubel_, Nov 20 2019
%o A135227 (Magma) [k eq 0 select n+1 else Binomial(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Nov 20 2019
%o A135227 (Sage)
%o A135227 def T(n, k):
%o A135227     if (k==0): return 1
%o A135227     else: return binomial(n, k)
%o A135227 [[T(n, k) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Nov 20 2019
%o A135227 (GAP)
%o A135227 T:= function(n,k)
%o A135227     if k=0 then return 1;
%o A135227     else return Binomial(n,k);
%o A135227     fi; end;
%o A135227 Flat(List([0..12], n-> List([0..n], k-> T(n,k) ))); # _G. C. Greubel_, Nov 20 2019
%Y A135227 Cf. A006127, A007318, A135225.
%K A135227 nonn,tabl
%O A135227 0,2
%A A135227 _Gary W. Adamson_, Nov 23 2007
%E A135227 More terms added by _G. C. Greubel_, Nov 20 2019