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A275329 a(n) = (2+[n/2])*n!/((1+[n/2])*[n/2]!^2). 1
2, 2, 3, 9, 8, 40, 25, 175, 84, 756, 294, 3234, 1056, 13728, 3861, 57915, 14300, 243100, 53482, 1016158, 201552, 4232592, 764218, 17577014, 2912168, 72804200, 11143500, 300874500, 42791040, 1240940160, 164812365, 5109183315, 636438060, 21002455980, 2463251010 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

FORMULA

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

a(n) = A057977(n)*A008619(n+2).

a(2*n+1) = (n+2)*binomial(2*n+1, n+1) = A189911(2*n+1).

a(2*n-3) = n*binomial(2*n-3, n-1) = A097070(n) for n>=2.

a(2*n+2) = (n+3)*binomial(2*n+2, n+1)/(n+2) = A038665(n).

MAPLE

a := n -> (2+iquo(n, 2))*n!/((1+iquo(n, 2))*iquo(n, 2)!^2):

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

PROG

(Sage)

def A275329():

    x, n, k = 1, 1, 2

    while True:

        yield x * k

        if is_odd(n):

            x *= n

        else:

            k += 1

            x = (x<<2)//(n+2)

        n += 1

a = A275329(); print([next(a) for _ in range(37)])

CROSSREFS

Cf. A038665, A056040, A057977, A097070, A189911.

Sequence in context: A278463 A276248 A322891 * A021821 A019234 A032172

Adjacent sequences:  A275326 A275327 A275328 * A275330 A275331 A275332

KEYWORD

nonn

AUTHOR

Peter Luschny, Sep 10 2016

STATUS

approved

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Last modified June 6 04:15 EDT 2020. Contains 334859 sequences. (Running on oeis4.)