

A119502


Triangle read by rows, T(n,k) = (nk)!, 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
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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 nth 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(nk): 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



