login
A038602
One half of convolution of central binomial coefficients A000984(n) with A000984(n+2), n >= 0.
1
3, 16, 73, 316, 1334, 5552, 22901, 93892, 383290, 1559680, 6331098, 25649976, 103758828, 419195552, 1691825933, 6822051092, 27488564498, 110691186272, 445487285678, 1792047789512, 7205785665908, 28963557761312
OFFSET
0,1
COMMENTS
Also convolution of A000346 with Catalan numbers but with C(0)=1 replaced by 3
FORMULA
a(n) = 2^(2*n+3)-(3*n+5)*C(n+1), C(n): Catalan numbers A000108.
G.f.: c(x)*(c(x)+2)/(1-4*x), where c(x) is G.f. for Catalan numbers.
a(n) ~ 2^(2*n+3) * (1-3/(2*sqrt(Pi*n))). - Vaclav Kotesovec, Mar 28 2014
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
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A012279 A037098 A316170 * A221829 A004303 A335625
KEYWORD
easy,nonn
STATUS
approved