A203483 a(n) = v(n+1)/v(n), where v = A203482.

3, 56, 19500, 267841728, 236189890379520, 19303349192505048268800, 199126474924007956512865886208000, 339543987407937097660189431863908761600000000, 121553118121801544803671246298148699436481551316864204800000

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..29

Formula

a(n) = Product_{k=1..n} (k! + (n+1)!). - G. C. Greubel, Aug 29 2023

From Vaclav Kotesovec, Nov 20 2023: (Start)

a(n) ~ (n+1)!^n.

a(n) ~ (2*Pi)^(n/2) * n^(n^2 + 3*n/2) / exp(n^2 - 13/12). (End)

Mathematica

(* First program *)
f[j_]:= j!; z = 10;
v[n_]:= Product[Product[f[k] + f[j], {j, k-1}], {k, 2, n}]
d[n_]:= Product[(i-1)!, {i, n}]   (* A000178 *)
Table[v[n], {n, z}]                (* A203482 *)
Table[v[n+1]/v[n], {n, z-1}]       (* this sequence *)
Table[v[n]/d[n], {n, 10}]          (* A203510 *)
(* Second program *)
Table[Product[k!+(n+1)!, {k, n}], {n, 15}] (* G. C. Greubel, Aug 29 2023 *)

Prog

(Magma) [(&*[Factorial(k) + Factorial(n+1): k in [1..n]]): n in [1..16]]; // G. C. Greubel, Aug 29 2023
(SageMath) [product(factorial(k) + factorial(n+1) for k in range(1, n+1)) for n in range(1, 16)] # G. C. Greubel, Aug 29 2023

Crossrefs

Cf. A000142, A093883, A203482, A203510, A323717.

Sequence in context: A132489 A350336 A344690 * A051227 A122548 A078728

Adjacent sequences: A203480 A203481 A203482 * A203484 A203485 A203486

Keyword

nonn

Author

Clark Kimberling, Jan 03 2012

Status

approved