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 A382436 #30 Jul 09 2025 05:08:47
%S A382436 1,1,1,1,3,1,1,6,6,1,1,9,17,9,1,1,12,36,36,12,1,1,15,64,101,64,15,1,1,
%T A382436 18,101,227,227,101,18,1,1,21,147,440,627,440,147,21,1,1,24,202,767,
%U A382436 1459,1459,767,202,24,1,1,27,266,1235,2994,3999,2994,1235,266,27,1
%N A382436 Triangle read by rows, defined by the two-variable g.f. 1/(1 - (y + 1)*x - y*x^2 - (y^2 + y)*x^3).
%C A382436 The original definition was "Decomposition of A077938".
%C A382436 Every row is symmetric.
%F A382436 G.f. 1/(1 - (y + 1)*x - y*x^2 - (y^2 + y)*x^3).
%F A382436 Sum_{k=0..n} (-1)^k * T(n,k) = A056594(n). - _Alois P. Heinz_, Mar 25 2025
%e A382436 Triangle begins:
%e A382436 1;
%e A382436 1, 1;
%e A382436 1, 3, 1;
%e A382436 1, 6, 6, 1;
%e A382436 1, 9, 17, 9, 1;
%e A382436 1, 12, 36, 36, 12, 1;
%e A382436 1, 15, 64, 101, 64, 15, 1;
%e A382436 1, 18, 101, 227, 227, 101, 18, 1;
%e A382436 1, 21, 147, 440, 627, 440, 147, 21, 1;
%e A382436 1, 24, 202, 767, 1459, 1459, 767, 202, 24, 1;
%e A382436 1, 27, 266, 1235, 2994, 3999, 2994, 1235, 266, 27, 1;
%e A382436 ...
%o A382436 (Sage)
%o A382436 y = polygen(QQ, 'y')
%o A382436 x = y.parent()[['x']].gen()
%o A382436 inverse = 1 + (-y - 1)*x - y*x^2 + (-y^2 - y)*x^3
%o A382436 gf = 1 / inverse
%o A382436 [list(u) for u in list(gf.O(11))]
%Y A382436 Similar to A008288, A103450, and A382444.
%Y A382436 Row sums are A077938.
%Y A382436 T(2n, n) gives A339565.
%Y A382436 Cf. A056594.
%K A382436 nonn,tabl
%O A382436 0,5
%A A382436 _F. Chapoton_, Mar 25 2025