1,2

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

Number of multiplications performed in a determinant. [From Mats O. Granvik (mgranvik(AT)abo.fi), Sep 12 2008]

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 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 27 2009]

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

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

S. R. Schmitt Determinants [From Mats O. Granvik (mgranvik(AT)abo.fi), Sep 12 2008]

a:=n->sum(n!, j=2..n):seq(a(n), n=1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2007

seq(sum(mul(j, j=1..n), k=2..n), n=1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 01 2007

a:=n->add((n!), j=1..n-1):seq(a(n), n=1..21); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 27 2008]

restart: 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); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 01 2009]

a[n_]:=1*(n+2)!-2*(n+1)!; ..and/or.. a[n_]:=n!*(n-1); [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 05 2008]

Table[Sum[n!, {i, 2, n}], {n, 1, 19}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]

(PARI) { f=1; for (n=1, 100, f*=n; write("b062119.txt", n, " ", f*(n - 1)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 02 2009]

Cf. A018931.

a(n)=2*A001286(n). Cf. A052849.

A001563 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 27 2008]

Sequence in context: A119921 A167747 A018931 this_sequence A052556 A052833 A144086

Adjacent sequences: A062116 A062117 A062118 this_sequence A062120 A062121 A062122

easy,nonn,new

Olivier Gerard (olivier.gerard(AT)gmail.com), Jun 13 2001

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