A175167 a(n) = Sum_{j=1..floor(n/2)} binomial(n+j-1,j-1).

0, 1, 1, 6, 7, 36, 45, 220, 286, 1365, 1820, 8568, 11628, 54264, 74613, 346104, 480700, 2220075, 3108105, 14307150, 20160075, 92561040, 131128140, 600805296, 854992152, 3910797436, 5586853480, 25518731280, 36576848168, 166871334960

Offset

1,4

Comments

As n -> infinity, a(2n)/a(2n-1) -> 9/2 and a(2n+1)/a(2n) -> 3/2.

Links

Robert Israel, Table of n, a(n) for n = 1..2415

Formula

a(n)=Sum(Binomial(n+j-1,j-1),(j,1,Floor[n/2])).

a(n) = floor(n/2) * C(n+floor(n/2), floor(n/2)) / (n+1). - Vaclav Kotesovec, Mar 02 2014

From Robert Israel, Feb 15 2019: (Start)(2*n+4)*a(n+1) = (3*n+2)*a(n) if n is even.

2*(n+2)*(n-1)*a(n+1) = 3*(n+1)*(3*n+1)*a(n) if n is odd. (End)

Maple

f:= proc(n) option remember;
  if n::odd then (3*n-1)/(2*n+2)*procname(n-1)
  else 3*n*(3*n-2)*procname(n-1)/(2*(n+1)*(n-2)) fi
end proc:
f(1):= 0: f(2):= 1: f(3):= 1:
map(f, [$1..40]); # Robert Israel, Feb 15 2019

Mathematica

f[n_] := Sum[ Binomial[n + j - 1, j - 1], {j, n/2}]; Array[f, 30]

Crossrefs

Sequence in context: A033043 A037411 A025626 * A027021 A013627 A248850

Adjacent sequences: A175164 A175165 A175166 * A175168 A175169 A175170

Keyword

nonn

Author

Roger L. Bagula, Dec 03 2010

Status

approved