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A238452 Second column of the extended Catalan triangle A189231. 2
0, 1, 2, 2, 8, 5, 30, 14, 112, 42, 420, 132, 1584, 429, 6006, 1430, 22880, 4862, 87516, 16796, 335920, 58786, 1293292, 208012, 4992288, 742900, 19315400, 2674440, 74884320, 9694845, 290845350, 35357670, 1131445440, 129644790, 4407922860, 477638700, 17194993200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..36.

FORMULA

Definition: a(n) = binomial(n+1, floor(n/2)+1) / (floor(n/2)+2) if n is odd else 2*binomial(n, floor(n/2)+1).

a(n) = A189231(n, 1).

a(n) = A238762(n+1, n-1).

a(2*n) = A162551(n).

a(2*n+1) = A000108(n+1).

a(n) = A057977(n+1) - A057977(n)*mod(n+1,2). - Peter Luschny, Aug 07 2016

MAPLE

a := proc(n) option remember;

  if n < 3 then return n fi;

  if n mod 2 = 0 then return n*a(n-1) fi;

  h := iquo(n, 2); n*a(n-1)/(h*(h+2)) end:

seq(a(n), n=0..36);

MATHEMATICA

t[n_, k_] /; (k > n || k < 0) = 0; t[n_, n_] = 1; t[n_, k_] := t[n, k] =

  t[n - 1, k - 1] + Mod[n - k, 2] t[n - 1, k] + t[n - 1, k + 1];

a[n_] := t[n, 1];

Table[a[n], {n, 0, 36}] (* Jean-François Alcover, Jul 10 2019 *)

PROG

(Sage)

def A238452():

    a = 1; n = 2

    yield 0

    while True:

        yield a

        a *= n

        if is_odd(n):

            a /= (n//2*(n//2+2))

        n += 1

a = A238452(); [next(a) for n in range(36)]

CROSSREFS

A000108, A057977, A162551, A189231.

Sequence in context: A241328 A223041 A024558 * A103238 A119999 A061828

Adjacent sequences:  A238449 A238450 A238451 * A238453 A238454 A238455

KEYWORD

nonn,easy

AUTHOR

Peter Luschny, Mar 01 2014

STATUS

approved

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)