1,3

For n>=2 also operation count to create all permutations of n distinct elements using Algorithm L (lexicographic permutation generation) from Knuth's The Art of Computer Programming, Vol. 4, chapter 7.2.1.2. Sequence gives number of loop repetitions of the j search loop in step L2. - Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 06 2003

This sequence shares divisibility properties with A000522; each of the primes in A072456 divide only a finite number of terms of this sequence. - T. D. Noe (noe(AT)sspectra.com), Jul 07 2005

D. E. Knuth: The Art of Computer Programming, Volume 4, Combinatorial Algorithms, Volume 4A, Enumeration and Backtracking. Pre-fascicle 2B, A draft of section 7.2.1.2: Generating all permutations. Available online; see link.

Tom Meuller, Prime and Composite Terms in Sloane's Sequence A056542, Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.3.

R. Sedgewick, Permutation generation methods, Computing Surveys, 9 (1977), 137-164.

T. D. Noe, Table of n, a(n) for n=1..100

D. E. Knuth, TAOCP Vol. 4, Pre-fascicle 2b (generating all permutations).

Tom Muller, Prime and Composite Terms in Sloane's Sequence A056542, Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.3. [Includes factorizations of a(1) through a(50)]

Hugo Pfoertner, FORTRAN implementation of Knuth's Algorithm L for lexicographic permutation generation.

Sam Wagstaff, Factorizations of a(51) through a(90)

a(n) = floor[(e-2)*n! ] = A002627(n)-n! = A000522(n)-2*n! = n!-A056543(n).

a:=n->sum((n-j)!*binomial(n,j),j=2..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 31 2006

a(4)=4*a(3)+1=4*4+1=17

a:=n->sum((n-j)!*binomial(n, j), j=2..n): seq(a(n), n=1..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 31 2006

a:=n->sum(n!/k!, k=2..n): seq(a(n), n=1..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 17 2007

tmp=0; Join[{tmp}, Table[tmp=n*tmp+1, {n, 2, 100}]] (T. D. Noe (noe(AT)sspectra.com), Jul 12 2005)

FoldList[ #1*#2 + 1 &, 0, Range[2, 21]] (from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 11 2005)

Cf. A079751 (same recursion formula, but starting from a(3)=0), A038155, A038156, A080047, A080048, A080049.

Cf. A007808, A002627.

Sequence in context: A104979 A081052 A020074 this_sequence A110508 A114190 A135168

Adjacent sequences: A056539 A056540 A056541 this_sequence A056543 A056544 A056545

easy,nonn

Henry Bottomley (se16(AT)btinternet.com), Jun 20 2000

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000