A038602 - OEIS

%I #16 Mar 29 2014 04:33:51

%S 3,16,73,316,1334,5552,22901,93892,383290,1559680,6331098,25649976,

%T 103758828,419195552,1691825933,6822051092,27488564498,110691186272,

%U 445487285678,1792047789512,7205785665908,28963557761312

%N One half of convolution of central binomial coefficients A000984(n) with A000984(n+2), n >= 0.

%C Also convolution of A000346 with Catalan numbers but with C(0)=1 replaced by 3

%H Fung Lam, <a href="/A038602/b038602.txt">Table of n, a(n) for n = 0..1500</a>

%F a(n) = 2^(2*n+3)-(3*n+5)*C(n+1), C(n): Catalan numbers A000108.

%F G.f.: c(x)*(c(x)+2)/(1-4*x), where c(x) is G.f. for Catalan numbers.

%F a(n) ~ 2^(2*n+3) * (1-3/(2*sqrt(Pi*n))).  - _Vaclav Kotesovec_, Mar 28 2014

%F Recurrence: n*(n+2)*a(n) = 2*(4*n^2 + 5*n - 1)*a(n-1) - 8*(n+1)*(2*n-1)*a(n-2). - _Vaclav Kotesovec_, Mar 28 2014

%t CoefficientList[Series[(1-Sqrt[1-4*x])/(2*x)*((1-Sqrt[1-4*x])/(2*x)+2)/(1-4*x), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 28 2014 *)

%Y Cf. A000108, A000346.

%K easy,nonn

%O 0,1

%A _Wolfdieter Lang_