A099869 Bisection of A014137.

1, 4, 23, 197, 2056, 23714, 290512, 3707852, 48760367, 656043857, 8987427467, 124936258127, 1757900019101, 24987199492705, 358268702159069, 5175497420902741, 75254198337177848, 1100534370899151722, 16176618251666906476, 238861285363295350240

Offset

0,2

Links

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

Formula

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

Recurrence: n*(2*n+1)*a(n) = 3*(2*n^2+13*n-8)*a(n-1) + 6*(74*n^2 - 305*n + 298)*a(n-2) - 28*(4*n-9)*(4*n-7)*a(n-3). - Vaclav Kotesovec, Oct 17 2012

a(n) ~ 2^(4*n+1/2)/(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): seq(a(n), n=0..20); # Emeric Deutsch

Mathematica

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

Prog

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

Crossrefs

Cf. A014137, A099975, A000108.

Sequence in context: A369140 A222454 A336948 * A369194 A365353 A265677

Adjacent sequences: A099866 A099867 A099868 * A099870 A099871 A099872

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 19 2004

Extensions

More terms from Emeric Deutsch, Dec 20 2004

Status

approved