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 A257372 #11 May 03 2015 02:48:29 %S A257372 1,6,6,15,30,21,42,15,30,33,66,1365,2730,3,6,255,510,399,798,165,330, %T A257372 69,138,1365,2730,3,6,435,870,7161,14322,255,510,3,6,959595,1919190,3, %U A257372 6,6765,13530,903,1806,345,690 %N A257372 a(n) = denominators of A255935(n) * triangle T(n,k) for Bernoulli(k+2), k=0 to n-1. %C A257372 Generally, A255935(n) multiplied by triangle T(n,k) for s(k), k=0 to n-1 yields an autosequence of the first kind (a sequence whose main diagonal is 0's). %C A257372 Here s(k) = 1/6, 0, -1/30, ... from A164555(n+2)/A027642(n+2). Hence %C A257372 0 = 0/1 %C A257372 1/6, 0 = 1/6 %C A257372 1/6, 0, 0 = 1/6 %C A257372 1/6, 0, -1/10, 0 = 1/15 %C A257372 1/6, 0, -1/5, 0, 0 =-1/30 %C A257372 ... . %C A257372 a(n) are the row sums denominators. %C A257372 Compare to A051716(n+2)/A051717(n+2). %C A257372 Hence the difference table %C A257372 0, 1/6, 1/6, 1/15, -1/30, -1/21, 1/42, ... %C A257372 1/6, 0, -1/10, -1/10, -1/70, 1/14, ... %C A257372 -1/6, -1/10, 0, 3/35, 3/35, ... %C A257372 1/15, 1/10, 3/35, 0, ... %C A257372 1/30, -1/70, -3/35, ... %C A257372 -1/21, -1/14, ... %C A257372 -1/42, ... %C A257372 ... . %F A257372 a(2n) = A002445(n). %F A257372 a(2n+3) = A001897(n+2). %F A257372 a(2n+2) = A040000(n) * a(2n+1). %Y A257372 Cf. A255935, A027641/A027642, A164555/A027642, A001897, A002445, A040000, A051716/A051717. %K A257372 nonn %O A257372 0,2 %A A257372 _Paul Curtz_, Apr 21 2015