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 A034273 #20 Sep 04 2025 01:55:04 %S A034273 0,1,19,186,1365,8540,48348,255816,1289739,6273135,29683225,137447310, %T A034273 625482585,2806282440,12443418600,54633668400,237871030860, %U A034273 1028260382994,4417404967206,18874729444340,80265980340370,339907420551336,1434074601137640,6030288337651760 %N A034273 a(n) = binomial(2*n+6,n+7)*(n^2+7*n+1)/(n+8) = f(n,n+6) where f is given in A034261. %H A034273 Michael De Vlieger, <a href="/A034273/b034273.txt">Table of n, a(n) for n = 0..1655</a> %F A034273 a(n) ~ 2^(2*n+6) * sqrt(n/Pi). - _Amiram Eldar_, Sep 04 2025 %t A034273 f[a_, b_] := Binomial[a + b, b + 1] (a b + a + 1)/(b + 2); Array[f[#, # + 6] &, 22, 0] (* _Michael De Vlieger_, Nov 08 2017 *) %o A034273 (PARI) A034273(n)=binomial(2*n+6, n+7)*(n^2+7*n+1)/(n+8) \\ _M. F. Hasler_, Nov 08 2017 %Y A034273 Cf. A034261 (main entry), A034263 - A034275 (other columns and diagonals n -> f(n,n+k)). %K A034273 nonn,changed %O A034273 0,3 %A A034273 _Clark Kimberling_ %E A034273 Corrected and extended by _N. J. A. Sloane_, Apr 21 2000 %E A034273 Edited by _M. F. Hasler_, Nov 08 2017