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 A034275 #32 Sep 04 2025 01:55:33 %S A034275 1,3,14,65,294,1302,5676,24453,104390,442442,1864356,7818538,32657884, %T A034275 135950700,564306840,2336457645,9652643910,39800950530,163830074100, %U A034275 673327275390,2763494696820,11327881630260,46381659765480,189711966348450,775232392541724,3165127107345252 %N A034275 a(n) = f(n,n-2) where f is given in A034261. %C A034275 Divisible by the Catalan numbers, by the explicit formula. - _F. Chapoton_, Jun 24 2021 %F A034275 a(n) = binomial(2*n-2,n-1)/n * (n^2-n+1). %F A034275 a(n) = binomial(2*n-2,n-1) + (n-1)*binomial(2*n-2,n). %F A034275 D-finite with recurrence n*a(n) + 2*(-6*n+7)*a(n-1) + 4*(11*n-24)*a(n-2) + 24*(-2*n+7)*a(n-3) = 0. - _R. J. Mathar_, Feb 10 2025 %F A034275 a(n) ~ 2^(2*n-2) * sqrt(n/Pi). - _Amiram Eldar_, Sep 04 2025 %t A034275 a[n_] := Binomial[2*n-2,n-1] * (n^2-n+1) / n; Array[a, 25] (* _Amiram Eldar_, Sep 04 2025 *) %o A034275 (Sage) %o A034275 [binomial(2*n-2,n-1)//n * (n**2-n+1) for n in range(1,8)] %o A034275 (PARI) a(n) = binomial(2*n-2,n-1)/n * (n^2-n+1); \\ _Michel Marcus_, Jun 24 2021 %Y A034275 Cf. A000108, A002061, A034261, A344191, A344228. %K A034275 nonn,easy,changed %O A034275 1,2 %A A034275 _Clark Kimberling_ %E A034275 Corrected and extended by _N. J. A. Sloane_, Apr 21 2000