login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A100630 Array read by antidiagonals: T(m,n) = Sum(1<=i<=m) [ i*(n-1+i)! ] 2
1, 2, 5, 6, 14, 23, 24, 54, 86, 119, 120, 264, 414, 566, 719, 720, 1560, 2424, 3294, 4166, 5039, 5040, 10800, 16680, 22584, 28494, 34406, 40319, 40320, 85680, 131760, 177960, 224184, 270414, 316646, 362879, 362880, 766080, 1174320, 1583280 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Inversion vector corresponding to T(m,n): ( n zeros , 1,2,3,...,m , zeros... )

These are the numbers of permutations (in reverse colexicographical order, compare A055089) that reverse a set of consecutive elements and leave all other elements unchanged. Permutation A(m,n) reverses all elements from n to m+n.

The former title of this sequence refers to finite tables of permutations in lexicographical order: "Triangle read by rows: row n gives the index number in the tables of permutations of order n+1, n+2, ... of the permutation in which the first n items are reversed and the remaining items are in order."

LINKS

Tilman Piesk, Table of n, a(n) for n = 1..2016

Tilman Piesk, Inversion (discrete mathematics) (Wikiversity)

EXAMPLE

T(3,2) = Sum( 1 <= i <= 3 ) [ i * (1+i)! ]

= 1*(1+1)! + 2*(1+2)! + 3*(1+3)!

= 1*2 + 2*6 + 3*24

= 86

PROG

MATLAB code is shown on the Wikiversity page.

Using Iverson's J language, A. p for a permutation p gives the row number in the table of permutations of order (length of p) which has p as its value. For example, q 0 4 9 6 7 5 1 11 8 10 2 3 A. q 13610272.

CROSSREFS

See A100711 for another version. Row 2 is A052649.

Sequence in context: A211369 A006596 A000092 * A275839 A057302 A237352

Adjacent sequences:  A100627 A100628 A100629 * A100631 A100632 A100633

KEYWORD

easy,nonn,tabl

AUTHOR

Eugene McDonnell (eemcd(AT)mac.com), Dec 03 2004

EXTENSIONS

Rewritten by Tilman Piesk, Jul 13 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 9 14:25 EST 2016. Contains 278971 sequences.