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 A356205 #5 Jul 29 2022 14:14:36 %S A356205 1,0,1,-1,0,3,0,-3,0,5,3,0,-15,0,35,0,15,0,-35,0,63,-5,0,105,0,-315,0, %T A356205 231,0,-35,0,315,0,-693,0,429,35,0,-315,0,3465,0,-3003,0,6435,0,315,0, %U A356205 -1155,0,9009,0,-6435,0,12155,-63,0,3465,0,-15015,0,45045,0,-109395,0,46189 %N A356205 T(n,k) are the numerators of the coefficients of the Legendre polynomials of degree n, with increasing exponents, where T(n,k) is a triangle read by rows. %e A356205 The triangle begins: %e A356205 1; %e A356205 0, 1; %e A356205 -1, 0, 3; %e A356205 0, -3, 0, 5; %e A356205 3, 0, -15, 0, 35; %e A356205 0, 15, 0, -35, 0, 63; %e A356205 -5, 0, 105, 0, -315, 0, 231; %e A356205 0, -35, 0, 315, 0, -693, 0, 429; %e A356205 35, 0, -315, 0, 3465, 0, -3003, 0, 6435; %e A356205 0, 315, 0, -1155, 0, 9009, 0, -6435, 0, 12155 %e A356205 . %e A356205 Fractions: %e A356205 \ k 0 1 2 3 4 5 6 7 8 %e A356205 n \ ------------------------------------------------------------------- %e A356205 0 | 1 . . . . . . . . %e A356205 1 | 0 1 . . . . . . . %e A356205 2 | -1/2 0 3/2 . . . . . . %e A356205 3 | 0 -3/2 0 5/2 . . . . . %e A356205 4 | 3/8 0 -15/4 0 35/8 . . . . %e A356205 5 | 0 15/8 0 -35/4 0 63/8 . . . %e A356205 6 | -5/16 0 105/16 0 -315/16 0 231/16 . . %e A356205 7 | 0 -35/16 0 315/16 0 -693/16 0 429/16 . %e A356205 8 | 35/128 0 -315/32 0 3465/64 0 -3003/32 0 6435/128 %o A356205 (PARI) for (n=0, 10, my(P=pollegendre(n,'x));for (j=0, n, print1(numerator(polcoef(P,j)),", ")); print()) %Y A356205 A356206 are the corresponding denominators. %Y A356205 Cf. A005187, A100258. %K A356205 sign,tabl,frac %O A356205 0,6 %A A356205 _Hugo Pfoertner_, Jul 29 2022