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 A060543 #14 Sep 24 2018 16:53:13
%S A060543 1,1,1,1,3,1,1,10,5,1,1,35,28,7,1,1,126,165,55,9,1,1,462,1001,455,91,
%T A060543 11,1,1,1716,6188,3876,969,136,13,1,1,6435,38760,33649,10626,1771,190,
%U A060543 15,1,1,24310,245157,296010,118755,23751,2925,253,17,1,1,92378,1562275
%N A060543 Triangle, read by antidiagonals, where T(n,k) = C(n+n*k+k, n*k+k).
%C A060543 Main diagonal is A108288. Antidiagonal sums is A108289. Inverse binomial transforms of each row give triangle A108290. G.f. of row n multiplied by (1-x)^(n+1) equals g.f. of row n of triangle A108267 (rows sums of A108267 equal (n+1)^n).
%H A060543 Harry J. Smith, <a href="/A060543/b060543.txt">Table of n, a(n) for n=0..252</a>
%F A060543 a(n) = A060539(n, k)/n = A007318(nk, k)/n = A060540(n, k)/A060540(n-1, k).
%e A060543 row 1: (2*n+1)/1!
%e A060543 row 2: (3*n+1)*(3*n+2)/2!
%e A060543 row 3: (4*n+1)*(4*n+2)*(4*n+3)/3!
%e A060543 row 4: (5*n+1)*(5*n+2)*(5*n+3)*(5*n+4)/4!
%e A060543 row 5: (6*n+1)*(6*n+2)*(6*n+3)*(6*n+4)*(6*n+5)/5!.
%e A060543 Table begins:
%e A060543 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
%e A060543 1,3,5,7,9,11,13,15,17,19,21,23,25,27,...
%e A060543 1,10,28,55,91,136,190,253,325,406,496,...
%e A060543 1,35,165,455,969,1771,2925,4495,6545,...
%e A060543 1,126,1001,3876,10626,23751,46376,82251,...
%e A060543 1,462,6188,33649,118755,324632,749398,...
%e A060543 1,1716,38760,296010,1344904,4496388,...
%o A060543 (PARI) T(n,k)=binomial(n+n*k+k,n*k+k)
%o A060543 (PARI) { i=0; write("b060543.txt", "0 1"); for (m=0, 20, for (k=0, m + 1, n=m - k + 1; write("b060543.txt", i++, " ", binomial(n + n*k + k, n*k + k))); ) } \\ _Harry J. Smith_, Jul 06 2009
%Y A060543 Cf. A108290, A108267, A108288, A108289, A060544 (row 2), A015219 (row 3).
%Y A060543 Rows include A000012, A001700, A025174. Columns include A000012, A005408, A060544. Main diagonal is A060545.
%K A060543 nonn,tabl
%O A060543 0,5
%A A060543 _Henry Bottomley_, Apr 02 2001
%E A060543 Entry revised by _Paul D. Hanna_, May 31 2005
%E A060543 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jun 17 2007