cp's OEIS Frontend

A038602 One half of convolution of central binomial coefficients A000984(n) with A000984(n+2), n >= 0.

%I A038602 #16 Mar 29 2014 04:33:51
%S A038602 3,16,73,316,1334,5552,22901,93892,383290,1559680,6331098,25649976,
%T A038602 103758828,419195552,1691825933,6822051092,27488564498,110691186272,
%U A038602 445487285678,1792047789512,7205785665908,28963557761312
%N A038602 One half of convolution of central binomial coefficients A000984(n) with A000984(n+2), n >= 0.
%C A038602 Also convolution of A000346 with Catalan numbers but with C(0)=1 replaced by 3
%H A038602 Fung Lam, <a href="/A038602/b038602.txt">Table of n, a(n) for n = 0..1500</a>
%F A038602 a(n) = 2^(2*n+3)-(3*n+5)*C(n+1), C(n): Catalan numbers A000108.
%F A038602 G.f.: c(x)*(c(x)+2)/(1-4*x), where c(x) is G.f. for Catalan numbers.
%F A038602 a(n) ~ 2^(2*n+3) * (1-3/(2*sqrt(Pi*n))).  - _Vaclav Kotesovec_, Mar 28 2014
%F A038602 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 A038602 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 A038602 Cf. A000108, A000346.
%K A038602 easy,nonn
%O A038602 0,1
%A A038602 _Wolfdieter Lang_