A084756 For n, k > 0, let T(n, k) be given by T(n, 1) = n and T(n, k+1) = k*T(n, k) + 1. Then a(n) = T(n, n).

1, 3, 9, 34, 161, 926, 6277, 48980, 432161, 4252330, 46152101, 547589912, 7050080545, 97878067886, 1457471241605, 23169742992076, 391638677761217, 7013544950036690, 132646182806388421, 2641922573730212000

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..445

Formula

T(n, k) = A000522(n-1) + (n-1)!*(k-1).

a(n) = A000522(n-1) + (n-1)!*(n-1).

Example

The table begins
  1, 2,  5, 16,  65, 326, 1957, ...
  2, 3,  7, 22,  89, 446, 2677, ...
  3, 4,  9, 28, 113, 566, 3397, ...
  4, 5, 11, 34, 137, 686, 4117, ...
  ...

Mathematica

a[n_]:= Floor[E*(n-1)!] +(n-1)*(n-1)! -Boole[n==1];
Table[a[n], {n, 40}] (* G. C. Greubel, May 13 2023 *)

Prog

(Magma)
A084756:= func< n | n eq 1 select 1 else Floor(Exp(1)*Factorial(n-1)) + (n-1)*Factorial(n-1) >;
[A084756(n): n in [1..40]]; // G. C. Greubel, May 13 2023
(SageMath)
def A084756(n): return floor(e*factorial(n-1)) + (n-1)*factorial(n-1) - int(n==1)
[A084756(n) for n in range(1, 41)] # G. C. Greubel, May 13 2023

Crossrefs

Cf. A000522, A084757.

Sequence in context: A349017 A246013 A219663 * A009578 A292292 A067787

Adjacent sequences: A084753 A084754 A084755 * A084757 A084758 A084759

Keyword

nonn,easy

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 17 2003

Extensions

Edited and extended by David Wasserman, Jan 05 2005

Status

approved