A132371 a(n) = n! - Sum_{j=1..n-1} j!.

1, 1, 3, 15, 87, 567, 4167, 34407, 316647, 3219687, 35878887, 435046887, 5704064487, 80428314087, 1213746099687, 19521187251687, 333363035571687, 6024361885107687, 114864714882483687, 2304476522241459687, 48529614677597619687, 1070348458111786419687

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..440

Formula

From G. C. Greubel, May 02 2021: (Start)

a(n) = A000142(n) - A007489(n-1).

a(n) = n! - A003422(n) + 1. (End)

Maple

seq(factorial(n)-(sum(factorial(j), j=1..n-1)), n=1..22); # Emeric Deutsch, May 26 2008

Mathematica

With[{fctrls=Range[30]!}, Table[fctrls[[n]]-Total[Take[fctrls, n-1]], {n, 30}]] (* Harvey P. Dale, Feb 27 2012 *)
Table[n! -Sum[j!, {j, n-1}], {n, 30}] (* G. C. Greubel, May 02 2021 *)

Prog

(Magma) A132371:= func< n | n eq 1 select 1 else  Factorial(n) - (&+[Factorial(j): j in [1..n-1]]) >;
[A132371(n): n in [1..30]]; // G. C. Greubel, May 02 2021
(Sage) [factorial(n) - sum(factorial(j) for j in (1..n-1)) for n in (1..30)] # G. C. Greubel, May 02 2021

Crossrefs

Cf. A000142, A003422, A007489, A140709.

Sequence in context: A089022 A359797 A246538 * A192989 A316666 A192253

Adjacent sequences: A132368 A132369 A132370 * A132372 A132373 A132374

Keyword

nonn

Author

Ben Branman, Nov 09 2007

Extensions

Corrected and extended by N. J. A. Sloane, Nov 11 2007

Better definition from Emeric Deutsch, May 26 2008

Status

approved