A099976 Bisection of A000984.

2, 20, 252, 3432, 48620, 705432, 10400600, 155117520, 2333606220, 35345263800, 538257874440, 8233430727600, 126410606437752, 1946939425648112, 30067266499541040, 465428353255261088, 7219428434016265740

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Formula

a(n) = binomial(4n+2, 2n+1). - Emeric Deutsch, Dec 20 2004

G.f.: 2*sqrt(2)/sqrt(1-16*x)/sqrt(1+sqrt(1-16*x)) = 2 + 60*x/(G(0)-30*x) where G(k)= 2*x*(4*k+3)*(4*k+5) + (2*k+3)*(k+1)- 2*x*(k+1)*(2*k+3)*(4*k+7)*(4*k+9)/G(k+1); (continued fraction, Euler's 1st kind, 1-step). - Sergei N. Gladkovskii, Jul 14 2012

G.f. A(x) satisfies A(x^2) = F'(x)/F(x), where F(x) = C(x)/C(-x) and C(x) = (1 - sqrt(1 - 4*x))/(2*x) is the g.f. of the Catalan numbers A000108. - Peter Bala, May 15 2023

Maple

seq(binomial(4*n+2, 2*n+1), n=0..20); # Emeric Deutsch, Dec 20 2004

Prog

(Magma) [Binomial(4*n+2, 2*n+1): n in [0..20]]; // Vincenzo Librandi, May 22 2011

Crossrefs

Cf. A000108, A000984, A001448.

Sequence in context: A197898 A293471 A109106 * A195157 A207151 A272568

Adjacent sequences: A099973 A099974 A099975 * A099977 A099978 A099979

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 19 2004

Extensions

More terms from Emeric Deutsch, Dec 20 2004

Status

approved