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 A386876 #17 Aug 06 2025 17:57:36 %S A386876 1,3,45,840,17325,378378,8576568,199536480,4732755885,113936715750, %T A386876 2775498395670,68263497731520,1692365881260600,42239049036433200, %U A386876 1060286332955364000,26747489892687315840,677672732203007541165,17234929348415589714750,439809863742901530128250 %N A386876 a(n) = (1/2) * (3*n)! / n!^3 for n > 0, a(0) = 1. %H A386876 Paolo Xausa, <a href="/A386876/b386876.txt">Table of n, a(n) for n = 0..650</a> %F A386876 a(n) = binomial(2*n - 1, n - 1)*binomial(3*n, n). %F A386876 a(n) = n! * [x^n] (1 + hypergeom([1/3, 2/3], [1, 1], 27*x)) / 2. %F A386876 a(n) ~ 3^(3*n+1/2)/(4*n*Pi). - _Stefano Spezia_, Aug 06 2025 %p A386876 egf := (1 + hypergeom([1/3, 2/3], [1, 1], 27*x)) / 2: %p A386876 ser := series(egf, x, 20): seq(n!*coeff(ser, x, n), n = 0.. 18); %t A386876 A386876[n_] := Binomial[2*n - 1, n - 1]*Binomial[3*n, n]; %t A386876 Array[A386876, 20, 0] (* _Paolo Xausa_, Aug 06 2025 *) %Y A386876 Cf. A006480, A386789. %K A386876 nonn,easy %O A386876 0,2 %A A386876 _Peter Luschny_, Aug 06 2025