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 A059045 #11 Jan 11 2015 04:33:19 %S A059045 0,1,0,1,1,0,1,3,1,0,1,6,5,1,0,1,10,17,7,1,0,1,15,49,34,9,1,0,1,21, %T A059045 129,142,57,11,1,0,1,28,321,547,313,86,13,1,0,1,36,769,2005,1593,586, %U A059045 121,15,1,0,1,45,1793,7108,7737,3711,985,162,17,1,0,1,55,4097,24604,36409 %N A059045 Square array T(n,k) read by antidiagonals where T(0,k) = 0 and T(n,k) = 1 + 2k + 3k^2 + ... + n*k^(n-1). %F A059045 T(n,k) = n*k^(n-1)+T(n-1, k) = (n*k^(n+1)-(n+1)*k^n+1)/(k-1)^2. %e A059045 0, 0, 0, 0, 0, 0, 0, 0, 0, ... %e A059045 1, 1, 1, 1, 1, 1, 1, 1, 1, ... %e A059045 1, 3, 5, 7, 9, 11, 13, 15, 17, ... %e A059045 1, 6, 17, 34, 57, 86, 121, 162, 209, ... %e A059045 1, 10, 49, 142, 313, 586, 985, 1534, 2257, ... %e A059045 1, 15, 129, 547, 1593, 3711, 7465, 13539, 22737, ... %e A059045 1, 21, 321, 2005, 7737, 22461, 54121, 114381, 219345, ... %e A059045 1, 28, 769, 7108, 36409, 131836, 380713, 937924, 2054353, ... %p A059045 A059045 := proc(n,k) %p A059045 if k = 1 then %p A059045 n*(n+1) /2 ; %p A059045 else %p A059045 (1+n*k^(n+1)-k^n*(n+1))/(k-1)^2 ; %p A059045 end if; %p A059045 end proc: # _R. J. Mathar_, Mar 29 2013 %Y A059045 Cf. A000004, A000012, A005408, A056109, A056578, A056579 (rows 1-6). %Y A059045 Cf. A057427, A000217, A000337, A014915, A014916, A014917, A014918, A014920 (columns 1-7). %K A059045 nonn,easy,tabl %O A059045 0,8 %A A059045 _Henry Bottomley_, Dec 18 2000