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 A377216 #15 May 10 2025 23:13:23
%S A377216 1,0,0,10,10,10,80,150,220,710,1620,2950,7010,16110,32560,70682,
%T A377216 156810,329290,698540,1507110,3189742,6725150,14279520,30141730,
%U A377216 63335960,133297362,279996460,586364410,1227337710,2566307410,5355970048,11166535430,23259949980,48389451510
%N A377216 Expansion of 1/(1 - 4*x^3/(1-x))^(5/2).
%H A377216 Vincenzo Librandi, <a href="/A377216/b377216.txt">Table of n, a(n) for n = 0..1500</a>
%F A377216 a(n) = (2*(n-1)*a(n-1) - (n-2)*a(n-2) + 2*(2*n+9)*a(n-3) - 2*(2*n+2)*a(n-4))/n for n > 3.
%F A377216 a(n) = Sum_{k=0..floor(n/3)} (-4)^k * binomial(-5/2,k) * binomial(n-2*k-1,n-3*k).
%F A377216 a(n) ~ n^(3/2) * 2^(n-3) / (3*sqrt(Pi)). - _Vaclav Kotesovec_, May 03 2025
%t A377216 Table[Sum[(-4)^k*Binomial[-5/2,k]*Binomial[n-2*k-1,n-3*k],{k,0,Floor[n/3]}],{n,0,35}] (* _Vincenzo Librandi_, May 10 2025 *)
%o A377216 (PARI) a(n) = sum(k=0, n\3, (-4)^k*binomial(-5/2, k)*binomial(n-2*k-1, n-3*k));
%o A377216 (Magma) R<x>:=PowerSeriesRing(Rationals(), 35); Coefficients(R!( 1/(1 - 4*x^3/(1-x))^(5/2))); // _Vincenzo Librandi_, May 10 2025
%Y A377216 Cf. A377199, A377215.
%Y A377216 Cf. A360309, A377213.
%K A377216 nonn
%O A377216 0,4
%A A377216 _Seiichi Manyama_, Oct 20 2024