A220371 a(n) = Product_{i=1..2*n} (4*i+2)*A060818(n).

1, 60, 30240, 17297280, 70572902400, 112634352230400, 518118020259840000, 1622745639453818880000, 53122201253160214855680000, 275173002491369912952422400000, 3520013047869603926487387340800000, 27244900990510734391012378017792000000

Offset: 0

Author

Peter Luschny, Dec 13 2012

Keywords

• nonn

Crossrefs

Cf. A009564, A060818, A103639, A193365.

Programs

Maple

a := proc(n): denom(binomial(1/2, iquo(n,2)))*product((4*i+2), i=1..2*n) end: seq(a(n), n=0..11); # Johannes W. Meijer, Dec 21 2012

Mathematica

a[n_] := 2^(2n)*Product[2i+1, {i, 1, 2n}]*GCD[n!, 2^n]; Table[a[n], {n, 0, 11}] (* Jean-François Alcover, Dec 21 2012 *)

Sage

@CachedFunction
def A005187(n): return A005187(n//2) + n if n > 0 else 0
def A220371(n): return mul(4*i+2 for i in (1..2*n)) << A005187(n//2)
[A220371(n) for n in range(12)]

Formula

a(n) = |A009564(n)|*A060818(n).

a(n) = 4*A193365(n)*a(n-1) with a(0) = 1. - Johannes W. Meijer, Dec 21 2012