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 A360856 #6 Feb 28 2023 03:54:49 %S A360856 1,1,2,6,16,48,140,424,1280,3920,12032,37184,115248,358624,1118784, %T A360856 3499584,10969344,34450944,108377984,341465344,1077300224,3403006464, %U A360856 10761447424,34065967104,107937899264,342293526016,1086339120128,3450236511232,10965437349888 %N A360856 a(n) = [x^n](1/2)*(1 + (2*x + 1)/sqrt(1 - 8*x^2*(x + 1))). %F A360856 a(n) = (4*(2*n^2 - 11*n + 15)*a(n - 3) + 4*(2*n^2 - 9*n + 9)*a(n - 2) + 2*(n - 3)*a(n - 1)) / (n^2 - 3*n) for n >= 4. %p A360856 gf := (1/2)*(1 + (2*x + 1)/sqrt(1 - 8*x^2*(x + 1))); %p A360856 ser := series(gf, x, 30): seq(coeff(ser, x, n), n = 0..28); %p A360856 # Recurrence: %p A360856 a := proc(n) option remember; if n < 4 then return [1, 1, 2, 6][n + 1] fi: %p A360856 (4*(2*n^2 - 11*n + 15)*a(n - 3) + 4*(2*n^2 - 9*n + 9)*a(n - 2) + 2*(n - 3)*a(n - 1)) / (n^2 - 3*n) end: seq(a(n), n = 0..28); %Y A360856 Cf. A360571. %K A360856 nonn %O A360856 0,3 %A A360856 _Peter Luschny_, Feb 28 2023