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 A367332 #7 Nov 14 2023 17:26:54 %S A367332 1,30,819,22188,599976,16212420,437948784,11828393820,319437445365, %T A367332 8626198419930,232935493710231,6289845008414760,169838331029620344, %U A367332 4585907100958922088,123825507087143633976,3343423515649756142760,90275493748778836055964 %N A367332 a(n) = 27^n * Sum_{k=0..n} binomial(1/3, k)^2. %C A367332 In general, for m>1, Sum_{k>=0} binomial(1/m,k)^2 = Gamma(1 + 2/m) / Gamma(1 + 1/m)^2. %F A367332 a(n) ~ 4 * Pi * 3^(3*n + 1/2) / Gamma(1/3)^3. %t A367332 Table[27^n*Sum[Binomial[1/3, k]^2, {k, 0, n}], {n, 0, 16}] %Y A367332 Cf. A358364, A367330, A367331, A367333. %K A367332 nonn %O A367332 0,2 %A A367332 _Vaclav Kotesovec_, Nov 14 2023