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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A119502 Triangle read by rows, T(n,k) = (n-k)!, for n>=0 and 0<=k<=n. 3
1, 1, 1, 2, 1, 1, 6, 2, 1, 1, 24, 6, 2, 1, 1, 120, 24, 6, 2, 1, 1, 720, 120, 24, 6, 2, 1, 1, 5040, 720, 120, 24, 6, 2, 1, 1, 40320, 5040, 720, 120, 24, 6, 2, 1, 1, 362880, 40320, 5040, 720, 120, 24, 6, 2, 1, 1, 3628800, 362880, 40320, 5040, 720, 120, 24, 6, 2, 1, 1, 39916800 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The reciprocal of each entry in a lower triangular readout of the exponential of a matrix whose entry {j+1,j} equals one (and all other entries are zero). Note all said entries are unit fractions (all numerators are one).

Denominators of unfinished fractional coefficients for polynomials A152650/A152656 = A009998/A119052. - Paul Curtz, Dec 13 2008

Multiplying the n-th diagonal by b_n with b_0 = 1 and then beheading the triangle provides a Gram matrix whose determinant is related to the reciprocal of e.g.f.s as presented in A133314. - Tom Copeland, Dec 04 2016

LINKS

Table of n, a(n) for n=0..66.

FORMULA

T(n,k) = A025581(n,k)!.

a(n) = Gamma(binomial(1 + floor((1/2) + sqrt(2*(1 + n))), 2) - n).

EXAMPLE

Triangle starts:

   1;

   1, 1;

   2, 1, 1;

   6, 2, 1, 1;

  24, 6, 2, 1, 1;

MATHEMATICA

Table[Gamma[Binomial[1 + Floor[(1/2) + Sqrt[2*(1 + n)]], 2] - n], {n, 0, 77}]

PROG

(MAGMA) [[Factorial(n-k): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Jun 18 2015

CROSSREFS

Cf. A025581.

Cf. A133314.

Sequence in context: A179380 A107106 A178249 * A142156 A136707 A179972

Adjacent sequences:  A119499 A119500 A119501 * A119503 A119504 A119505

KEYWORD

easy,nonn,tabl

AUTHOR

Joseph Biberstine (jrbibers(AT)indiana.edu), May 26 2006

EXTENSIONS

Name edited by Peter Luschny, Jun 17 2015

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 19 04:10 EDT 2019. Contains 326109 sequences. (Running on oeis4.)