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 A382403 #11 Mar 24 2025 10:22:02
%S A382403 1,2,36,980,33040,1268568,53105976,2364239592,110206067400,
%T A382403 5323547715200,264576141331216,13458185494436592,697931136204820336,
%U A382403 36789784967375728400,1966572261077797609200,106400946932857148590800,5817987630644593688220600,321105713814359742307398480
%N A382403 a(n) = Sum_{k=0..n} A039599(n,k)^3.
%C A382403 Let b_k(n) = Sum_{j=0..n} A039599(n,j)^k. b_1(n) = binomial(2*n,n) = A000984(n) and b_2(n) = binomial(4*n,2*n)/(2*n+1) = A048990(n).
%H A382403 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 A382403 a(n) = binomial(2*n,n) * (4 * binomial(2*n,n)^2 - 3 * A112029(n)).
%o A382403 (PARI) a039599(n, k) = (2*k+1)/(n+k+1)*binomial(2*n, n-k);
%o A382403 a(n) = sum(k=0, n, a039599(n, k)^3);
%Y A382403 Cf. A000984, A048990.
%Y A382403 Cf. A039599, A112029.
%K A382403 nonn
%O A382403 0,2
%A A382403 _Seiichi Manyama_, Mar 24 2025