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A127625 Triangle T(n,k) = binomial(n-1,k-1)*A001511(k), 1<=k<=n, read by rows.

%I A127625 #13 Jan 02 2025 09:34:47
%S A127625 1,1,2,1,4,1,1,6,3,3,1,8,6,12,1,1,10,10,30,5,2,1,12,15,60,15,12,1,1,
%T A127625 14,21,105,35,42,7,4,1,16,28,168,70,112,28,32,1,1,18,36,252,126,252,
%U A127625 84,144,9,2,1,20,45,360,210,504,210,480,45,20,1
%N A127625 Triangle T(n,k) = binomial(n-1,k-1)*A001511(k), 1<=k<=n, read by rows.
%C A127625 Column k of Pascal's triangle is multiplied by the k-th entry of the ruler sequence.
%H A127625 James C. McMahon, <a href="/A127625/b127625.txt">Table of n, a(n) for n = 1..10000</a>
%F A127625 T(n,n) = A001511(n).
%e A127625 First few rows of the triangle are:
%e A127625 1;
%e A127625 1, 2;
%e A127625 1, 4, 1;
%e A127625 1, 6, 3, 3;
%e A127625 1, 8, 6, 12, 1;
%e A127625 1, 10, 10, 30, 5, 2;
%e A127625 1, 12, 15, 60, 15, 12, 1;
%e A127625 ...
%t A127625 T[n_,k_]:=Binomial[n-1,k-1]*IntegerExponent[2k,2];Table[T[n,k],{n,9},{k,n}]//Flatten (* _James C. McMahon_, Jan 01 2025 *)
%Y A127625 Cf. A106461 (row sums), A001511.
%K A127625 nonn,tabl
%O A127625 1,3
%A A127625 _Gary W. Adamson_, Jan 20 2007
%E A127625 a(46)-a(66) from _James C. McMahon_, Jan 01 2025