A238452 Second column of the extended Catalan triangle A189231.

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

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, and 2*binomial(n, floor(n/2)+1) otherwise.

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)*((n+1) mod 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

Cf. 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