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 A383715 #21 May 07 2025 09:40:44
%S A383715 1,1,-1,1,-2,-1,1,-5,-5,1,1,-12,-30,12,1,1,-29,-174,174,29,-1,1,-70,
%T A383715 -1015,2436,1015,-70,-1,1,-169,-5915,34307,34307,-5915,-169,1,1,-408,
%U A383715 -34476,482664,1166438,-482664,-34476,408,1,1,-985,-200940,6791772,39618670,-39618670,-6791772,200940,985,-1
%N A383715 Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows, where T(n,k) = (-1)^floor((k+1)/2) * A099927(n,k).
%F A383715 Let f(n, x) be defined as f(n, x) = Sum_{k=0..n} T(n,k) * x^k.
%F A383715 f(n, x) = exp( -Sum_{k>=1} Pell(n*k)/Pell(k) * x^k/k ).
%F A383715 Sum_{k>=0} A099927(n+k,n) * x^k = 1/f(n+1, x).
%e A383715 Triangle starts:
%e A383715 1;
%e A383715 1, -1;
%e A383715 1, -2, -1;
%e A383715 1, -5, -5, 1;
%e A383715 1, -12, -30, 12, 1;
%e A383715 1, -29, -174, 174, 29, -1;
%e A383715 1, -70, -1015, 2436, 1015, -70, -1;
%e A383715 1, -169, -5915, 34307, 34307, -5915, -169, 1;
%e A383715 ...
%o A383715 (PARI) pell(n) = ([2, 1; 1, 0]^n)[2, 1];
%o A383715 p(n, k) = prod(j=0, k-1, pell(n-j));
%o A383715 a099927(n, k) = p(n, k)/p(k, k);
%o A383715 T(n, k) = (-1)^((k+1)\2)*a099927(n, k);
%Y A383715 Cf. A055870, A099927.
%K A383715 sign,tabl
%O A383715 0,5
%A A383715 _Seiichi Manyama_, May 07 2025