A303607 a(n) = floor(C(n + 1/2)), where C = A000108.

0, 1, 3, 8, 24, 74, 237, 781, 2630, 9020, 31375, 110442, 392685, 1408249, 5087870, 18501347, 67662072, 248703832, 918291072, 3404396173, 12667520643, 47292077070, 177093735411, 665005047259, 2503548413211, 9447352502685, 35728169464702, 135390957971502, 514026687891806

Offset

0,3

Comments

A000108 interleaved with this sequence gives floor(C(n/2)).

Links

Paolo P. Lava, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ 2^(2*n + 1) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Apr 27 2018

Example

C(n + 1/2)*Pi gives: 2^3/3, 2^6/(3*5), 2^10/(3*5*7), 2^13/(5*7*9), 2^18/(5*7*9*11), 2^21/(7*9*11*13), 2^25/(5*7*9*11*13), ...

Maple

P:=proc(n) floor(evalf(binomial(2*n+1, n+1/2)/(n+3/2), 1200)); end: seq(P(i), i=0..28); # Paolo P. Lava, May 03 2018

Mathematica

Table[Floor[CatalanNumber[n + 1/2]], {n, 0, 30}]

Crossrefs

Cf. A000108, A000796.

Sequence in context: A046919 A291886 A275856 * A281872 A046342 A238977

Adjacent sequences: A303604 A303605 A303606 * A303608 A303609 A303610

Keyword

nonn

Author

Bruno Berselli, Apr 27 2018

Status

approved