A063079 Bisection of A001790.

1, 5, 63, 429, 12155, 88179, 1300075, 9694845, 583401555, 4418157975, 67282234305, 514589420475, 15801325804719, 121683714103007, 1879204156221315, 14544636039226909, 1804857108504066435

Offset: 1

Author

N. J. A. Sloane, Aug 07 2001

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Petros Hadjicostas, Proof of the claim A334907(n)/n! = a(n+1)/A060818(n), 2020.

Crossrefs

Cf. A001790, A060818, A334907. Other bisection gives A061548.

Programs

Maple

seq(numer(binomial(2*n-3/2,-1/2)), n=1..20);

Mathematica

Numerator[Binomial[2Range[20]-3/2,-(1/2)]] (* Harvey P. Dale, Feb 27 2012 *)

Formula

Numerators of binomial(2*n-3/2, -1/2).

Because A334907(n)/n! = a(n+1)/A060818(n) for n >= 0, the o.g.f. of a(n+1)/A060818(n), for n >= 0, is (sqrt(1 + sqrt(8*s)) - sqrt(1 - sqrt(8*s)))/sqrt(8*s * (1 - 8*s)), which is the e.g.f. of A334907 (see the link above for a proof). - Petros Hadjicostas, May 16 2020

Extensions

More terms from Vladeta Jovovic, Aug 07 2001