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 A377195 #10 May 09 2025 00:53:57
%S A377195 1,10,90,710,5250,37072,253330,1688640,11039370,71049200,451429880,
%T A377195 2837585940,17674206130,109224234420,670398280520,4090210956596,
%U A377195 24823230801450,149941593205140,901881446152120,5404072772837620,32269536034506456,192087243952281920
%N A377195 Expansion of 1/(1 - 4*x*(1+x)^2)^(5/2).
%F A377195 a(0) = 1, a(1) = 10, a(2) = 90; a(n) = (2*(2*n+3)*a(n-1) + 8*(n+3)*a(n-2) + 2*(2*n+9)*a(n-3))/n.
%F A377195 a(n) = Sum_{k=0..n} (-4)^k * binomial(-5/2,k) * binomial(2*k,n-k).
%t A377195 a[n_]:=Sum[(-4)^k*Binomial[-5/2,k]Binomial[2*k,n-k],{k,0,n}]; Array[a,22,0] (* _Stefano Spezia_, May 08 2025 *)
%o A377195 (PARI) a(n) = sum(k=0, n, (-4)^k*binomial(-5/2, k)*binomial(2*k, n-k));
%Y A377195 Cf. A137635, A377194, A377196.
%K A377195 nonn
%O A377195 0,2
%A A377195 _Seiichi Manyama_, Oct 19 2024