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 A081130 #18 Sep 08 2022 08:45:09
%S A081130 0,0,0,0,0,0,0,0,1,0,0,0,1,3,0,0,0,1,6,6,0,0,0,1,9,24,10,0,0,0,1,12,
%T A081130 54,80,15,0,0,0,1,15,96,270,240,21,0,0,0,1,18,150,640,1215,672,28,0,0,
%U A081130 0,1,21,216,1250,3840,5103,1792,36,0,0,0,1,24,294,2160,9375,21504,20412,4608,45,0
%N A081130 Square array of binomial transforms of (0,0,1,0,0,0,...), read by antidiagonals.
%C A081130 Rows, of the square array, are three-fold convolutions of sequences of powers.
%H A081130 G. C. Greubel, <a href="/A081130/b081130.txt">Antidiadoganal rows n = 0..50, flattened</a>
%F A081130 T(n, k) = k^(n-2)*binomial(n, 2), with T(n, 0) = 0 (square array).
%F A081130 T(n, n) = A081131(n).
%F A081130 Rows have g.f. x^3/(1-k*x)^n.
%F A081130 From _G. C. Greubel_, May 14 2021: (Start)
%F A081130 T(k, n-k) = (n-k)^(k-2)*binomial(k,2) with T(n, n) = 0 (antidiagonal triangle).
%F A081130 Sum_{k=0..n} T(n, n-k) = A081197(n). (End)
%e A081130 The array begins as:
%e A081130 0, 0, 0, 0, 0, 0, ...
%e A081130 0, 0, 0, 0, 0, 0, ...
%e A081130 0, 1, 1, 1, 1, 1, ... A000012
%e A081130 0, 3, 6, 9, 12, 15, ... A008585
%e A081130 0, 6, 24, 54, 96, 150, ... A033581
%e A081130 0, 10, 80, 270, 640, 1250, ... A244729
%e A081130 The antidiagonal triangle begins as:
%e A081130 0;
%e A081130 0, 0;
%e A081130 0, 0, 0;
%e A081130 0, 0, 1, 0;
%e A081130 0, 0, 1, 3, 0;
%e A081130 0, 0, 1, 6, 6, 0;
%e A081130 0, 0, 1, 9, 24, 10, 0;
%t A081130 Table[If[k==n, 0, (n-k)^(k-2)*Binomial[k, 2]], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, May 14 2021 *)
%o A081130 (Magma) [k eq n select 0 else (n-k)^(k-2)*Binomial(k,2): k in [0..n], n in [0..12]]; // _G. C. Greubel_, May 14 2021
%o A081130 (Sage) flatten([[0 if (k==n) else (n-k)^(k-2)*binomial(k,2) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, May 14 2021
%o A081130 (PARI)
%o A081130 T(n, k)=if (k==0, 0, k^(n-2)*binomial(n, 2));
%o A081130 seq(nn) = for (n=0, nn, for (k=0, n, print1(T(k, n-k), ", ")); );
%o A081130 seq(12) \\ _Michel Marcus_, May 14 2021
%Y A081130 Main diagonal: A081131.
%Y A081130 Rows: A000012 (n=2), A008585 (n=3), A033581 (n=4), A244729 (n=5).
%Y A081130 Columns: A000217 (k=1), A001788 (k=2), A027472 (k=3), A038845 (k=4), A081135 (k=5), A081136 (k=6), A027474 (k=7), A081138 (k=8), A081139 (k=9), A081140 (k=10), A081141 (k=11), A081142 (k=12), A027476 (k=15).
%K A081130 easy,nonn,tabl
%O A081130 0,14
%A A081130 _Paul Barry_, Mar 08 2003
%E A081130 Term a(5) corrected by _G. C. Greubel_, May 14 2021