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A237884 a(n) = (n!*m)/(m!*(m+1)!) where m = floor(n/2). 1
0, 0, 1, 3, 4, 20, 15, 105, 56, 504, 210, 2310, 792, 10296, 3003, 45045, 11440, 194480, 43758, 831402, 167960, 3527160, 646646, 14872858, 2496144, 62403600, 9657700, 260757900, 37442160, 1085822640, 145422675, 4508102925, 565722720, 18668849760, 2203961430 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..34.

FORMULA

a(2*n) = A001791(n).

a(2*n+1) = A000917(n-1).

a(n) = n^mod(n,2)*binomial(2*floor(n/2),floor(n/2)-1).

a(n) = A162246(n, n+2) = n!/((n-ceil((n+2)/2))!*floor((n+2)/2)!)) if n>1 else 0.

a(n) = A056040(n)*floor(n/2)/(floor(n/2)+1).

a(n) + A056040(n) = A057977(n).

G.f.: -((p-1-x*(p-1+2*x*(2*p-3+x*(3+4*x-2*p))))/(2*x^2*p^3)), where p=sqrt(1-4*x^2). - Benedict W. J. Irwin, Aug 15 2016

MAPLE

A237884 := proc(n) m := iquo(n, 2); (n!*m)/(m!*(m+1)!) end;

seq(A237884(n), n = 0..34);

MATHEMATICA

CoefficientList[Series[-((-1 + Sqrt[1 - 4 x^2] -x (-1 + Sqrt[1 - 4 x^2] +

2 x (-3 + 2 Sqrt[1 - 4 x^2] +x (3 + 4 x - 2 Sqrt[1 - 4 x^2]))))/

(2 x^2 (1 - 4 x^2)^(3/2))), {x, 0, 30}], x] (* Benedict W. J. Irwin, Aug 15 2016 *)

Table[(n! #)/(#! (# + 1)!) &@ Floor[n/2], {n, 0, 34}] (* Michael De Vlieger, Aug 15 2016 *)

PROG

(Sage)

def A237884():

    r, s, n = 1, 0, 0

    while true:

        yield s

        n += 1

        r *= 4/n if is_even(n) else n

        s = r * (n//2)/(n//2+1)

a = A237884(); [a.next() for i in range(35)]

CROSSREFS

Sequence in context: A041561 A050214 A256605 * A256532 A051719 A240970

Adjacent sequences:  A237881 A237882 A237883 * A237885 A237886 A237887

KEYWORD

nonn

AUTHOR

Peter Luschny, Feb 14 2014

STATUS

approved

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Last modified June 26 20:37 EDT 2019. Contains 324380 sequences. (Running on oeis4.)