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A100852 Triangle read by rows: T(n,k) = 2^k * 3^n, 0 <= k <= n.

%I A100852 #16 Feb 16 2025 08:32:55
%S A100852 1,3,6,9,18,36,27,54,108,216,81,162,324,648,1296,243,486,972,1944,
%T A100852 3888,7776,729,1458,2916,5832,11664,23328,46656,2187,4374,8748,17496,
%U A100852 34992,69984,139968,279936,6561,13122,26244,52488,104976,209952,419904,839808
%N A100852 Triangle read by rows: T(n,k) = 2^k * 3^n, 0 <= k <= n.
%C A100852 T(n,0) = A000244(n); T(n,n) = A000400(n) = A100851(n,n);
%C A100852 T(n,1) = A008776(n) for n>0;
%C A100852 T(n,2) = A003946(n+1) for n>1;
%C A100852 T(n,3) = A005051(n+1) for n>2;
%C A100852 T(n,n-1) = A081341(n+1) for n>0;
%C A100852 row sums give A016137.
%H A100852 Michael De Vlieger, <a href="/A100852/b100852.txt">Table of n, a(n) for n = 0..10010</a> (Rows 0 <= n <= 140).
%H A100852 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmoothNumber.html">Smooth Number</a>
%F A100852 G.f.: 1/((1 - 3*x)(1 - 6*x*y)). - _Ilya Gutkovskiy_, Jun 03 2017
%e A100852 Triangle begins:
%e A100852    1;
%e A100852    3,   6;
%e A100852    9,  18,  36;
%e A100852   27,  54, 108, 216;
%e A100852   81, 162, 324, 648, 1296;
%e A100852 ...
%t A100852 Table[2^k*3^n, {n, 0, 140}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Mar 06 2017 *)
%o A100852 (PARI) for(n=0, 8, for(k=0, n, print1(2^k*3^n", "))) \\ _Satish Bysany_, Mar 06 2017
%Y A100852 Cf. A100851, A003586, A065333(T(n, k))=1.
%K A100852 nonn,tabl
%O A100852 0,2
%A A100852 _Reinhard Zumkeller_, Nov 20 2004