A123637 a(n) = 1 + 1*n + 1*n*2 + 1*n*2*(n-1) + 1*n*2*(n-1)*3 + 1*n*2*(n-1)*3*(n-2) + ... + n!*(n+1)!.

1, 4, 23, 238, 4285, 120056, 4807699, 259889218, 18207958073, 1603405689580, 173263178533711, 22534190356771094, 3471514311529290613, 625057269686305463008, 130043797443156653379275

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

Formula

a(n) = Sum_{k=0..2*n} (floor((k + 2)/2)! * n!)/((n - floor((k + 1)/2))!). - G. C. Greubel, Oct 26 2017

Example

a(n) equals the sum of (2n+1) terms:
a(0) = 1;
a(1) = 1 + 1*1 + 1*1*2 = 4;
a(2) = 1 + 1*2 + 1*2*2 + 1*2*2*1 + 1*2*2*1*3 = 23;
a(3) = 1 + 1*3 + 1*3*2 + 1*3*2*2 + 1*3*2*2*3 + 1*3*2*2*3*1 + 1*3*2*2*3*1*4 = 238.

Mathematica

Join[{1}, Table[Sum[(Floor[(k + 2)/2]! * n!)/((n - Floor[(k + 1)/2])!), {k, 0, 2*n}], {n, 1, 50}]] (* G. C. Greubel, Oct 26 2017 *)

Prog

(PARI) {a(n)=sum(k=1, 2*n+1, prod(j=1, k, ((j+1)\2)*(j%2)+(n+1-(j\2))*((j-1)%2)))}

Crossrefs

Cf. A123636.

Sequence in context: A292312 A316083 A326501 * A293510 A234595 A327367

Adjacent sequences: A123634 A123635 A123636 * A123638 A123639 A123640

Keyword

nonn

Author

Paul D. Hanna, Oct 04 2006

Status

approved