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 A382057 #12 Apr 01 2025 22:38:20
%S A382057 8,-37,181,-865,4105,-19441,92017,-435457,2060641,-9751105,46142785,
%T A382057 -218350081,1033243777,-4889362177,23136710401,-109484089345,
%U A382057 518084273665,-2451601105921,11601100993537,-54896999325697,259775389992961,-1229270344003585,5816969724063745,-27526196280360961
%N A382057 Z-sequence for the Riordan triangle A125166.
%C A382057 For the Z-sequence of a Riordan trangle R(G(x), F(x)=x*Fhat(x)) see the first W. Lang link in A006232, where also references are given,
%C A382057 The Z-sequence implies a recurrence formula for R(n, 0) using the previous row entries of R.
%C A382057 R(n, 0) = Sum_{j=0..n-1} Z(j)*R(n-1, j), for n >= 1, and R(0, 0) = G(0), usually 1.
%C A382057 The o.g.f. of the Z-sequence of R is GZ(y) = (1/F^{[-1]}(y))*(1 - 1/G(F^{[-1]}(y))), with the composition inverse F^{[-1]} of F.
%H A382057 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-7,-12,-6).
%F A382057 O.g.f.: (8 + 19*x + 18*x^2 + 6*x^3)/((1 + x)*(1 + 6*x+ 6*x^2)).
%e A382057 The Riordan triangle A125166 has row n = 3 [64, 36, 10, 1], hence R(0, 4) = 8*64 - 37*36 + 10*181 - 1*865 = 125 = 5^3.
%t A382057 LinearRecurrence[{-7,-12,-6},{8,-37,181,-865},24] (* _Stefano Spezia_, Mar 26 2025 *)
%Y A382057 Cf. A006232, A125166.
%K A382057 sign,easy
%O A382057 0,1
%A A382057 _Wolfdieter Lang_, Mar 25 2025