cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A105291 Triangle read by rows: T(m,n) = binomial(m!,n), m>=0, 0 <= n <= m!.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 6, 15, 20, 15, 6, 1, 1, 24, 276, 2024, 10626, 42504, 134596, 346104, 735471, 1307504, 1961256, 2496144, 2704156, 2496144, 1961256, 1307504, 735471, 346104, 134596, 42504, 10626, 2024, 276, 24, 1, 1, 120, 7140, 280840, 8214570, 190578024
Offset: 0

Views

Author

N. J. A. Sloane, Sep 03 2010, following a suggestion from R. H. Hardin, Aug 31 2010

Keywords

Comments

This is the number of nXm arrays with each row a permutation of 1..m, and rows in lexicographically strictly increasing order.
For row 0, remember that 0!=1.

Examples

			Triangle begins:
[1, 1],
[1, 1],
[1, 2, 1],
[1, 6, 15, 20, 15, 6, 1],
[1, 24, 276, 2024, 10626, 42504, 134596, 346104, 735471, 1307504, 1961256, 2496144, 2704156, 2496144, 1961256, 1307504, 735471, 346104, 134596, 42504, 10626, 2024, 276, 24, 1],
...

Links

Crossrefs

See A180397 for another version.
Cf. A007318 (Pascal's triangle), A086687, A109892.

Programs

  • Mathematica
    Flatten[Table[Binomial[m!,n],{m,0,5},{n,0,m!}]] (* Harvey P. Dale, Apr 16 2013 *)

A109893 a(n) = least integer of the form (n!-1)(n!-2)...(n!-k)/n!.

Original entry on oeis.org

10, 8855, 182637273, 187913191983517, 16299312030218924938187, 173083581780047419995380839040497, 300642522445723721070400405660702004585922575, 109109034687569422667248530075550555291614316919209445960161, 10269669381215922304236773275682334781908421087118493054965910074350106387039
Offset: 3

Views

Author

Amarnath Murthy, Jul 13 2005

Keywords

Comments

k <= n. Subsidiary sequence: n such that k < n.

Examples

			a(3) = 5*4*3/6 =10. a(4) = 23*22*21*20/4! = 8855.

Crossrefs

Cf. A109892.

Programs

  • Maple
    A109893 := proc(n) local k ; for k from 1 to n do if mul( n!-i,i=1..k) mod ( n! ) = 0 then RETURN( mul(n!-i,i=1..k)/n!) ; fi ; od: end: seq(A109893(n),n=3..12) ; # R. J. Mathar, Feb 13 2008

Extensions

Corrected and extended by R. J. Mathar, Feb 13 2008
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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