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 A373392 #26 Jun 17 2024 10:02:41
%S A373392 1,0,0,1,-2,3,-4,7,-18,51,-136,339,-814,1935,-4620,11111,-26842,64923,
%T A373392 -156944,379067,-915078,2208711,-5331476,12870639,-31072754,75018195,
%U A373392 -181113240,437248771,-1055610782,2548462143,-6152518684,14853483127,-35859484938,86572485771
%N A373392 Inverse binomial transform of A135318.
%H A373392 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-4,-5,-2,2).
%F A373392 G.f.: (1 + 4*x + 5*x^2 + 3*x^3) / ( (1 + 2*x - x^2) * (1 + 2*x + 2*x^2) ).
%F A373392 E.g.f.: 1/6*exp(-x)*(2*cos(-x) + 4*cosh(sqrt(2)*-x) - 3*sqrt(2)*sinh(sqrt(2)*-x)).
%F A373392 a(n) = -4*a(n-1) - 5*a(n-2) - 2*a(n-3) + 2*a(n-4), for n > 4.
%F A373392 a(n) = (-1)^(n+1)*(A000129(n-2) + 2*A009545(n-2))/3, for n > 2. - _Thomas Scheuerle_, Jun 04 2024
%F A373392 a(n) = A373358(n-3) - (-1)^n*A009545(n+2) for n > 2.
%t A373392 LinearRecurrence[{-4, -5, -2, 2}, {1, 0, 0, 1}, 35] (* _Amiram Eldar_, Jun 09 2024 *)
%o A373392 (PARI) a(n) = ((-([-2,-1;-1, 0]^(n-2))[2, 1]) - 2*((I-1)^(n-4) + (-I-1)^(n-4)))/3; \\ _Thomas Scheuerle_, Jun 04 2024
%Y A373392 Cf. A000129, A009545, A135318, A373358.
%K A373392 sign,easy
%O A373392 0,5
%A A373392 _Paul Curtz_, Jun 03 2024