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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).
2
1, 3, 9, 34, 161, 926, 6277, 48980, 432161, 4252330, 46152101, 547589912, 7050080545, 97878067886, 1457471241605, 23169742992076, 391638677761217, 7013544950036690, 132646182806388421, 2641922573730212000
OFFSET
1,2
LINKS
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
Sequence in context: A349017 A246013 A219663 * A009578 A292292 A067787
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