A099975 Bisection of A014137.

2, 9, 65, 626, 6918, 82500, 1033412, 13402697, 178405157, 2423307047, 33453694487, 467995871777, 6619846420553, 94520750408709, 1360510918810437, 19720133460129650, 287590328749420958, 4216819865806452984, 62127422576288648840, 919286657093271150630

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = sum(binomial(2k, k)/(k+1), k=0..2n+1). - Emeric Deutsch, Dec 20 2004

Recurrence: (n+1)*(2*n+1)*a(n) = 3*(2*n^2 + 15*n - 1)*a(n-1) + 6*(74*n^2 - 231*n + 164)*a(n-2) - 28*(4*n-7)*(4*n-5)*a(n-3). - Vaclav Kotesovec, Oct 17 2012

a(n) ~ 2^(4*n+5/2)/(3*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 17 2012

Maple

a:=n->sum(binomial(2*k, k)/(k+1), k=0..2*n+1): seq(a(n), n=0..20); # Emeric Deutsch, Dec 20 2004

Mathematica

Table[Sum[Binomial[2k, k]/(k+1), {k, 0, 2*n+1}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 17 2012 *)

Prog

(PARI) a(n)=sum(k=0, 2*n+1, binomial(2*k, k)/(k+1)); \\ Joerg Arndt, May 12 2013

Crossrefs

Cf. A014137, A099975.

Cf. A000108.

Sequence in context: A071300 A062395 A352986 * A292976 A334315 A334263

Adjacent sequences: A099972 A099973 A099974 * A099976 A099977 A099978

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 19 2004

Extensions

More terms from Emeric Deutsch, Dec 20 2004

Status

approved