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 A034267 #23 Sep 04 2025 01:57:57 %S A034267 0,1,7,39,196,930,4257,19019,83512,361998,1553630,6615686,27992472, %T A034267 117823940,493768485,2061580275,8580127920,35611376790,147447066690, %U A034267 609200868210,2512267906200,10342848445020,42516521451690,174535009040574,715599131576976,2930673247541900 %N A034267 a(n) = f(n,n) where f is given in A034261. %F A034267 Conjecture D-finite with recurrence -(n+2)*(11*n-7)*a(n) + 2*(23*n^2+44*n+30)*a(n-1) - 4*(n+5)*(2*n-3)*a(n-2) = 0. - _R. J. Mathar_, Feb 10 2025 %F A034267 From _Amiram Eldar_, Sep 04 2025: (Start) %F A034267 a(n) = binomial(2*n, n+1)*(n^2+n+1)/(n+2); %F A034267 a(n) ~ 2^(2*n) * sqrt(n/Pi). (End) %p A034267 A034261 := proc(n, k) binomial(n+k, k+1)*(n*k+n+1)/(k+2); end; %p A034267 seq( A034261(n,n),n=0..40) ; # _R. J. Mathar_, Feb 10 2025 %t A034267 a[n_] := Binomial[2*n, n+1]*(n^2 + n + 1)/(n + 2); Array[a, 25, 0] (* _Amiram Eldar_, Sep 04 2025 *) %Y A034267 Cf. A034261. %K A034267 nonn,changed %O A034267 0,3 %A A034267 _Clark Kimberling_ %E A034267 Corrected and extended by _N. J. A. Sloane_, Apr 21 2000