A390137 - OEIS

%I #24 Nov 24 2025 10:06:59

%S 1,3,21,85,495,2223,12039,56763,296685,1434805,7358781,36088473,

%T 183146521,905332005,4566776625,22678765605,113994908415,567640935855,

%U 2847279814575,14201053809075,71143115574195,355177319996535,1777990698946395,8881720064004375,44440847923704975

%N Expansion of 1/((1-5*x) * sqrt(1+4*x)).

%H Seiichi Manyama, <a href="/A390137/b390137.txt">Table of n, a(n) for n = 0..1000</a>

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

%F n*a(n) = (n+2)*a(n-1) + 10*(2*n-1)*a(n-2).

%F a(n) = 5*a(n-1) + (-1)^n * A000984(n).

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

%Y Cf. A000984, A091520, A144635.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 24 2025