A112332 a(n) = Product_{k=0..n-1} k!*binomial(2k,k).

1, 1, 2, 24, 2880, 4838400, 146313216000, 97339256340480000, 1683704371913057894400000, 873705178746128941669416960000000, 15414977576506278044562764045746176000000000, 10334857226047177887548812577909403133201612800000000000

Offset

0,3

Links

Table of n, a(n) for n=0..11.

Formula

a(n)=denominator(Product{k=0..n-1, (2k+1)!/(n+k)!}).

G.f.: 1+ x*G(0)/2, where G(k)= 1 + 1/(1 - 1/(1 + 1/((2*k+2)!/(k+1)!)/x/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 15 2013

a(n) ~ A^(1/2) * 2^(n^2 - n/2 - 7/24) * n^(n^2/2 - n/2 + 1/24) / exp(3*n^2/4 - n/2 + 1/24), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Jul 11 2015

From Alois P. Heinz, Jun 30 2022: (Start)

a(n) = Product_{i=1..n-1} Product_{j=i..n-1} (i+j).

a(n) = A110131(n). (End)

Maple

seq(mul(mul((j+k), j=1..k), k=1..n), n=-1..9); # Zerinvary Lajos, Sep 21 2007

Mathematica

Table[Product[(2*k)!/k!, {k, 0, n-1}], {n, 0, 10}] (* Vaclav Kotesovec, Jul 11 2015 *)

Crossrefs

Cf. A005130, A110131.

Sequence in context: A007079 A083697 A110131 * A101339 A111428 A111429

Adjacent sequences: A112329 A112330 A112331 * A112333 A112334 A112335

Keyword

easy,nonn

Author

Paul Barry, Sep 04 2005

Status

approved