This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A164942 #32 Sep 08 2022 08:45:47
%S A164942 1,3,-1,9,-6,1,27,-27,9,-1,81,-108,54,-12,1,243,-405,270,-90,15,-1,
%T A164942 729,-1458,1215,-540,135,-18,1,2187,-5103,5103,-2835,945,-189,21,-1,
%U A164942 6561,-17496,20412,-13608,5670,-1512,252,-24,1,19683,-59049,78732,-61236,30618,-10206,2268,-324,27,-1
%N A164942 Triangle, read by rows, T(n,k) = (-1)^k*binomial(n, k)*3^(n-k).
%C A164942 Rows sum up to A000079, antidiagonals sum up to A001906.
%C A164942 Triangle, read by rows, given by [3,0,0,0,0,0,0,0,...] DELTA [ -1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Sep 02 2009
%C A164942 Row n: expansion of (3-x)^n. - _Philippe Deléham_, Oct 09 2011
%C A164942 Essentially the same as the inverse of A027465, but with opposite signs in every other row. - _M. F. Hasler_, Feb 17 2020
%C A164942 The inverse of A027465 is (-1)^(n-k)*binomial(n, k)*3^(n - k). - _G. C. Greubel_, Feb 17 2020
%H A164942 G. C. Greubel, <a href="/A164942/b164942.txt">Rows n = 0..100 of triangle, flattened</a>
%F A164942 T(n,k) = (-1)^n*(Inverse of A027465).
%F A164942 T(n,k) = 3*T(n-1,k) - T(n-1,k-1). - _Philippe Deléham_, Oct 09 2011
%F A164942 G.f.: 1/(1-3*x+x*y). - _R. J. Mathar_, Aug 11 2015
%e A164942 Begins as triangle:
%e A164942 1;
%e A164942 3, -1;
%e A164942 9, -6, 1;
%e A164942 27, -27, 9, -1;
%e A164942 81, -108, 54, -12, 1;
%e A164942 243, -405, 270, -90, 15, -1;
%p A164942 seq(seq( (-1)^k*binomial(n, k)*3^(n-k), k=0..n), n=0..10); # _G. C. Greubel_, Feb 17 2020
%t A164942 With[{m = 9}, CoefficientList[CoefficientList[Series[1/(1-3*x+x*y), {x, 0, m}, {y, 0, m}], x], y]] // Flatten (* _Georg Fischer_, Feb 17 2020 *)
%o A164942 (Magma) [(-1)^k*Binomial(n, k)*3^(n-k): k in [0..n], n in [0..10]]; // _G. C. Greubel_, Feb 17 2020
%o A164942 (Sage) [[(-1)^k*binomial(n, k)*3^(n-k) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Feb 17 2020
%Y A164942 Cf. A000079, A001906, A027465.
%K A164942 sign,tabl
%O A164942 0,2
%A A164942 _Mark Dols_, Sep 01 2009
%E A164942 More terms from _Philippe Deléham_, Oct 09 2011
%E A164942 a(46) corrected by _Georg Fischer_, Feb 17 2020
%E A164942 Title changed by _G. C. Greubel_, Feb 17 2020