A240879 Self-convolution of Sum(binomial(2*n, i), i=0..n).

1, 6, 31, 150, 699, 3178, 14198, 62604, 273235, 1182786, 5085666, 21743956, 92522206, 392066340, 1655432524, 6967724312, 29245179267, 122442487474, 511487386730, 2132341655556, 8873167793578, 36861311739308, 152895342950196, 633290273209000, 2619653638855214, 10823294835350388

Offset: 0

Author

Fung Lam, Apr 13 2014

Keywords

• nonn

Links

• Fung Lam, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A032443.

Programs

Mathematica

CoefficientList[Series[((1/Sqrt[1-4*x] + 1/(1-4*x))/2)^2, {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 16 2014 *)

Formula

G.f. = (g.f. of A032443)^2.

n*a(n) = 32*(2*n-3)*a(n-3) + 48*(1-n)*a(n-2) + 6*(2*n-1)*a(n-1).

Asymptotics: a(n) ~ 2^(2*n)*((n+2)/4 + sqrt(n/Pi)).

Recurrence: (n-2)*n*a(n) = 2*n*(4*n-7)*a(n-1) - 8*(n-1)*(2*n-1)*a(n-2). - Vaclav Kotesovec, Apr 16 2014