A279881 a(n) = A168467(n) * Sum_{k=0..n}(2^k*(k!)^2 / (2*k+1)!).

1, 8, 1056, 5529600, 2040024268800, 82038030902231040000, 512596445591262883479552000000, 671373457257855830831011844849664000000000, 238977230623673235057124486022413812190150656000000000000

Offset: 0

Author

Daniel Suteu, Dec 21 2016

Keywords

• nonn
• easy

Links

• Daniel Suteu, Table of n, a(n) for n = 0..19

Crossrefs

Cf. A168467.

Programs

Mathematica

Table[Product[((2 k + 2) (2 k + 3))^(n - k), {k, 0, n}] Sum[(2^j*(j!)^2/(2 j + 1)!), {j, 0, n}], {n, 0, 8}] (* Michael De Vlieger, Dec 22 2016 *)

PARI

a(n) = prod(k=1, n, (2*k+1)!) * sum(k=0, n, 2^k * (k!)^2 / (2*k+1)!)

Formula

a(n) ~ Pi/2 * A168467(n).

a(0) = 1, a(n) = a(n-1) * (2*n + 1)! + 2^n * (n!)^2 * A168467(n-1).