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A175167 a(n) = Sum_{j=1..floor(n/2)} binomial(n+j-1,j-1). 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 26 19:13 EDT 2021. Contains 347670 sequences. (Running on oeis4.)