

A068943


a(n) = f(n, n, n), where f is the generalized super falling factorial (see comments for definition.).


3




OFFSET

1,2


COMMENTS

f(x, p, r) = Product_{m = 1..p} (xm+1)^binomial(m+r2, m1), for x > 0, x >= p >= 0, r > 0. f is a generalization of both the multilevel factorial A066121(n, k) and the falling factorial A068424(x, n). f(n, n, 1) = n! and f(n, n, 2) = the superfactorial A000178(n). In general f(n, n, r) = A066121(n+r, r+1). f(x, p, 1) = A068424(x, p) and f(x, p, r+1) = Product{i = 0..p1} f(xi, pi, r).


LINKS

Table of n, a(n) for n=1..6.


FORMULA

a(n) = Product_{m = 1..n} (nm+1)^binomial(m+n2, m1)


EXAMPLE

a(3)=24 since (41)^binomial(1+32,11) * (42)^binomial(2+32,21) * (43)^binomial(3+32,31) = 3^1 * 2^3 * 1 = 24.


MAPLE

f := (x, p, r)>`if`(r<>0, `if`(p>0, product((xm+1)^binomial(m+r2, m1), m=1..p), 1), x); f(n, n, n);


CROSSREFS

Sequence in context: A123851 A258824 A120122 * A100815 A159932 A100010
Adjacent sequences: A068940 A068941 A068942 * A068944 A068945 A068946


KEYWORD

easy,nonn


AUTHOR

Francois Jooste (phukraut(AT)hotmail.com), Mar 09 2002


EXTENSIONS

Edited by David Wasserman, Mar 14 2003


STATUS

approved



