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 A382668 #22 Apr 05 2025 10:53:25 %S A382668 2,10,33,108,359,1214,4169,14508,51064,181492,650522,2348856,8535921, %T A382668 31197430,114601065,422891340,1566903060,5827192140,21743726430, %U A382668 81383916840,305465105790,1149489049644,4335921660522,16391329697528,62091796219904,235656705875304 %N A382668 a(n) = C(n+1) - C(n-1) - 2*C(n-2) where C(n) = A000108(n) are the Catalan numbers. %F A382668 a(n) = [x^n] ((2*x^3 + x^2 - 1)*sqrt(1 - 4*x) - 4*x^3 - 3*x^2 - 2*x + 1)/(2*x^2). - _Peter Luschny_, Apr 03 2025 %p A382668 gf := ((2*x^3 + x^2 - 1)*sqrt(1 - 4*x) - 4*x^3 - 3*x^2 - 2*x + 1)/(2*x^2): %p A382668 ser := series(gf, x, 30): seq(coeff(ser, x, n), n = 2..27); # _Peter Luschny_, Apr 03 2025 %t A382668 a[n_]:=CatalanNumber[n+1]-CatalanNumber[n-1]-2CatalanNumber[n-2];Array[a,26,2] (* _James C. McMahon_, Apr 05 2025 *) %o A382668 (SageMath) %o A382668 C = catalan_number %o A382668 [C(n + 1) - C(n - 1) - 2 * C(n - 2) for n in range(2, 28)] %Y A382668 Cf. A000108, A026012, A280891. %K A382668 nonn,easy %O A382668 2,1 %A A382668 _F. Chapoton_, Apr 02 2025