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A062119 a(n) = n! * (n-1). 17
0, 2, 12, 72, 480, 3600, 30240, 282240, 2903040, 32659200, 399168000, 5269017600, 74724249600, 1133317785600, 18307441152000, 313841848320000, 5690998849536000, 108840352997376000, 2189611807358976000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For n > 0, a(n) = number of permutations of length n+1 that have 2 predetermined elements nonadjacent; e.g., for n=2, the permutations with, say, 1 and 2 nonadjacent are 132 and 231, therefore a(2)=2. - Jon Perry, Jun 08 2003

Number of multiplications performed when computing the determinant of an n X n matrix by definition. - Mats Granvik, Sep 12 2008

Sum of the length of all cycles (excluding fixed points) in all permutations of [n]. - Olivier Gérard, Oct 23 2012

Number of permutations of n distinct objects (ABC...) 1 (one) times >>("-", A, AB, ABC, ABCD, ABCDE, ..., ABCDEFGHIJK, infinity) and one after the other to resemble motif: A (1) AB (1-1), AAB (2-1), AAAB (3-1), AAAAB (4-1), AAAAAB (5-1), AAAAAAB (6-1), AAAAAAAB (7-1), AAAAAAAAB (8-1) etc.,>> "1(one) fixed point". Example:motif: AAAB (or BBBA) 12 * one (1) fixed point etc. Let: AAAB ................ 'A'BCD 1. 'A'BDC 2. 'A'CBD 3. ACDB 'A'DBC 4. 'A'DCB B'A'CD 5. B'A'DC 6. BCAD 7. BCDA BD'A'C 8. BDCA C'A'BD 9. C'A'DB CB'A'D 10. CBDA CDAB CDBA D'A'BC 11. DACB DB'A'C 12. DBCA DCAB DCBA. - Zerinvary Lajos, Nov 27 2009 (does anybody understand what this is supposed to say? - Joerg Arndt, Jan 10 2015)

a(n) is the number of ways to arrange n books on two bookshelves so that each shelf receives at least one book. - Geoffrey Critzer, Feb 21 2010

a(n) = number whose factorial base representation (A007623) begins with digit {n-1} and is followed by n-1 zeros. Viewed in that base, this sequence looks like this: 0, 10, 200, 3000, 40000, 500000, 6000000, 70000000, 800000000, 9000000000, A0000000000, B00000000000, ... (where "digits" A and B stand for placeholder values 10 and 11 respectively). - Antti Karttunen, May 07 2015

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..100

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.

S. R. Schmitt Determinants [From Mats Granvik, Sep 12 2008]

Index entries for sequences related to factorial base representation

FORMULA

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

E.g.f.: x^2/(1-x)^2. - Geoffrey Critzer, Feb 21 2010

a(n) = 2 * A001286(n).

a(n) = A001563(n) - A000142(n). - Antti Karttunen, May 07 2015, hinted by crossref left by Lajos.

MAPLE

G(x):=x^2/(1-x)^2: f[0]:=G(x): for n from 1 to 19 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=1..19); # Zerinvary Lajos, Apr 01 2009

MATHEMATICA

a[n_]:=1*(n+2)!-2*(n+1)!; (* or *) a[n_]:=n!*(n-1); (* Vladimir Joseph Stephan Orlovsky, Dec 05 2008 *)

PROG

(PARI) { f=1; for (n=1, 100, f*=n; write("b062119.txt", n, " ", f*(n - 1)) ) } \\ Harry J. Smith, Aug 02 2009

(PARI) a(n) = n!*(n-1); \\ Altug Alkan, May 04 2018

(Haskell)

a062119 n = (n - 1) * a000142 n  -- Reinhard Zumkeller, Aug 27 2012

(Scheme) (define (A062119 n) (* (- n 1) (A000142 n))) ;; Antti Karttunen, May 07 2015

CROSSREFS

Column 2 of A257503 (apart from initial zero. Equally, row 2 of A257505).

Cf. A001286 (same sequence divided by 2).

Cf. A000142, A007623, A018931, A052849.

Cf. A001563. - Zerinvary Lajos, Aug 27 2008

Cf. sequences with formula (n + k)*n! listed in A282466.

Sequence in context: A279154 A167747 A018931 * A181966 A052556 A052833

Adjacent sequences:  A062116 A062117 A062118 * A062120 A062121 A062122

KEYWORD

easy,nonn

AUTHOR

Olivier Gérard, Jun 13 2001

EXTENSIONS

Last term a(19) corrected by Harry J. Smith, Aug 02 2009

STATUS

approved

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Last modified November 18 01:19 EST 2018. Contains 317279 sequences. (Running on oeis4.)