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 A382394 #24 Mar 24 2025 10:21:57
%S A382394 1,1,9,190,5705,204876,8209278,354331692,16140234825,765868074400,
%T A382394 37525317999884,1886768082651816,96906387191038334,
%U A382394 5066711735118128200,268954195756648761900,14464077426547576156440,786729115199980286001225,43219452658242723841261800
%N A382394 a(n) = Sum_{k=0..n} A128899(n,k)^3.
%C A382394 Let b_k(n) = Sum_{j=0..n} A128899(n,j)^k. b_1(n) = binomial(2*n-1,n) = A088218(n) and b_2(n) = A024492(n-1) for n > 0.
%H A382394 Pedro J. Miana, Hideyuki Ohtsuka, and Natalia Romero, <a href="http://arxiv.org/abs/1602.04347">Sums of powers of Catalan triangle numbers</a>, arXiv:1602.04347 [math.NT], 2016.
%F A382394 a(n) = binomial(2*n,n)/2 * A183069(n) for n > 0.
%F A382394 a(n) = A003161(2*n-1) for n > 0.
%o A382394 (PARI) a128899(n, k) = binomial(2*n-2, n-k)-binomial(2*n-2, n-k-2);
%o A382394 a(n) = sum(k=0, n, a128899(n, k)^3);
%Y A382394 Cf. A024492, A088218.
%Y A382394 Cf. A001700, A003161, A128899, A183069.
%K A382394 nonn
%O A382394 0,3
%A A382394 _Seiichi Manyama_, Mar 24 2025