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 A131086 #9 Nov 09 2019 01:11:42 %S A131086 1,3,1,1,5,1,3,5,7,1,1,9,11,9,1,3,9,21,19,11,1,1,13,29,41,29,13,1,3, %T A131086 13,43,69,71,41,15,1,1,17,55,113,139,113,55,17,1,3,17,73,167,253,251, %U A131086 169,71,19,1,1,21,89,241,419,505,419,241,89,21,1,3,21,111,329 %N A131086 Triangle read by rows: T(n,k) = 2*binomial(n,k) - (-1)^(n-k) (0 <= k <= n). %C A131086 Row sums = A051049 starting (1, 4, 7, 16, 31, 64, ...). %F A131086 G.f. = G(t,z) = (1 + 3z - tz - 2tz^2)/((1+z)(1-tz)(1-z-tz)). - _Emeric Deutsch_, Jun 21 2007 %e A131086 First few rows of the triangle are %e A131086 1; %e A131086 3, 1; %e A131086 1, 5, 1; %e A131086 3, 5, 7, 1; %e A131086 1, 9, 11, 9, 1; %e A131086 3, 9, 21, 19, 11, 1; %e A131086 1, 13, 29, 41, 29, 13, 1; %e A131086 ... %p A131086 T := proc (n, k) if k <= n then 2*binomial(n, k)-(-1)^(n-k) else 0 end if end proc: for n from 0 to 11 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - _Emeric Deutsch_, Jun 21 2007 %Y A131086 Cf. A000012, A051049. %K A131086 nonn,tabl %O A131086 0,2 %A A131086 _Gary W. Adamson_, Jun 14 2007 %E A131086 More terms from _Emeric Deutsch_, Jun 21 2007 %E A131086 Sequence corrected by _N. J. A. Sloane_, Sep 30 2007