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 A377213 #18 May 08 2025 12:31:59
%S A377213 1,0,0,6,6,6,36,66,96,266,576,1026,2246,4866,9516,19598,41286,83526,
%T A377213 170048,351378,716850,1458098,2984028,6087270,12380900,25224222,
%U A377213 51356400,104380510,212164362,431148222,875353220,1776567762,3604752672,7310374010,14819370480,30033014994
%N A377213 Expansion of 1/(1 - 4*x^3/(1-x))^(3/2).
%H A377213 Vincenzo Librandi, <a href="/A377213/b377213.txt">Table of n, a(n) for n = 0..1800</a>
%F A377213 a(n) = (2*(n-1)*a(n-1) - (n-2)*a(n-2) + 2*(2*n+3)*a(n-3) - 2*(2*n-2)*a(n-4))/n for n > 3.
%F A377213 a(n) = Sum_{k=0..floor(n/2)} (2*k+1) * binomial(2*k,k) * binomial(n-2*k-1,n-3*k).
%F A377213 a(n) ~ sqrt(n) * 2^(n-2) / sqrt(Pi). - _Vaclav Kotesovec_, May 03 2025
%t A377213 Table[Sum[(2*k+1)*Binomial[2*k,k]*Binomial[n-2*k-1,n-3*k],{k,0,Floor[n/3]}],{n,0,35}] (* _Vincenzo Librandi_, May 08 2025 *)
%o A377213 (PARI) a(n) = sum(k=0, n\3, (2*k+1)*binomial(2*k, k)*binomial(n-2*k-1, n-3*k));
%o A377213 (Magma) R<x>:=PowerSeriesRing(Rationals(), 35); Coefficients(R!( 1/(1 - 4*x^3/(1-x))^(3/2))); // _Vincenzo Librandi_, May 08 2025
%Y A377213 Cf. A377197, A377204.
%Y A377213 Cf. A360309, A377216.
%K A377213 nonn
%O A377213 0,4
%A A377213 _Seiichi Manyama_, Oct 20 2024