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 A377215 #15 May 08 2025 15:27:42
%S A377215 1,0,10,10,80,150,640,1550,5190,13870,41912,115650,333490,925970,
%T A377215 2607540,7220062,20053700,55230870,152005380,416295350,1137980678,
%U A377215 3100453710,8429823180,22862244210,61882724100,167159512794,450739897980,1213298505770,3260824389510
%N A377215 Expansion of 1/(1 - 4*x^2/(1-x))^(5/2).
%H A377215 Vincenzo Librandi, <a href="/A377215/b377215.txt">Table of n, a(n) for n = 0..1500</a>
%F A377215 a(n) = (2*(n-1)*a(n-1) + (3*n+14)*a(n-2) - 2*(2*n-1)*a(n-3))/n for n > 2.
%F A377215 a(n) = Sum_{k=0..floor(n/2)} (-4)^k * binomial(-5/2,k) * binomial(n-k-1,n-2*k).
%F A377215 a(n) ~ n^(3/2) * 2^(3*n - 1/2) / (3 * 17^(5/4) * sqrt(Pi) * (sqrt(17) - 1)^(n - 5/2)). - _Vaclav Kotesovec_, May 03 2025
%t A377215 Table[Sum[(-4)^k*Binomial[-5/2,k]*Binomial[n-k-1,n-2*k],{k,0,Floor[n/2]}],{n,0,35}] (* _Vincenzo Librandi_, May 08 2025 *)
%o A377215 (PARI) a(n) = sum(k=0, n\2, (-4)^k*binomial(-5/2, k)*binomial(n-k-1, n-2*k));
%o A377215 (Magma) R<x>:=PowerSeriesRing(Rationals(), 35); Coefficients(R!( 1/(1 - 4*x^2/(1-x))^(5/2))); // _Vincenzo Librandi_, May 08 2025
%Y A377215 Cf. A377199, A377216.
%Y A377215 Cf. A026585, A377204.
%K A377215 nonn
%O A377215 0,3
%A A377215 _Seiichi Manyama_, Oct 20 2024