%I #13 Oct 26 2024 07:02:58
%S 1,10,80,570,3790,24062,147780,885190,5199560,30065870,171623328,
%T 969151710,5422863630,30105497970,165993714540,909770119914,
%U 4959840748350,26912374137150,145411035749600,782681600883950,4198276264607290,22448626776903450,119690255236279100
%N Expansion of 1/(1 - 4*x/(1-x))^(5/2).
%F a(0) = 1; a(n) = 2 * Sum_{k=0..n-1} (5-3*k/n) * a(k).
%F a(n) = (2*(3*n+2)*a(n-1) - 5*(n-2)*a(n-2))/n for n > 1.
%F a(n) = Sum_{k=0..n} (-4)^k * binomial(-5/2,k) * binomial(n-1,n-k).
%F a(n) ~ 128 * n^(3/2) * 5^(n - 5/2) / (3*sqrt(Pi)). - _Vaclav Kotesovec_, Oct 26 2024
%o (PARI) a(n) = sum(k=0, n, (-4)^k*binomial(-5/2, k)*binomial(n-1, n-k));
%Y Cf. A085362, A377197, A377200.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 19 2024