A377216 - OEIS

%I #8 Oct 20 2024 08:32:49

%S 1,0,0,10,10,10,80,150,220,710,1620,2950,7010,16110,32560,70682,

%T 156810,329290,698540,1507110,3189742,6725150,14279520,30141730,

%U 63335960,133297362,279996460,586364410,1227337710,2566307410,5355970048,11166535430,23259949980,48389451510

%N Expansion of 1/(1 - 4*x^3/(1-x))^(5/2).

%F 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 a(n) = Sum_{k=0..floor(n/3)} (-4)^k * binomial(-5/2,k) * binomial(n-2*k-1,n-3*k).

%o (PARI) a(n) = sum(k=0, n\3, (-4)^k*binomial(-5/2, k)*binomial(n-2*k-1, n-3*k));

%Y Cf. A377199, A377215.

%Y Cf. A360309, A377213.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Oct 20 2024