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A068943 a(n) = f(n, n, n), where f is the generalized super falling factorial (see comments for definition.). 3
1, 2, 24, 331776, 2524286414780230533120, 18356962141505758798331790171539976807981714702571497465907439808868887035904000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

f(x, p, r) = Product_{m = 1..p} (x-m+1)^binomial(m+r-2, m-1), for x > 0, x >= p >= 0, r > 0. f is a generalization of both the multi-level 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..p-1} f(x-i, p-i, r).

LINKS

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

FORMULA

a(n) = Product_{m = 1..n} (n-m+1)^binomial(m+n-2, m-1)

EXAMPLE

a(3)=24 since (4-1)^binomial(1+3-2,1-1) * (4-2)^binomial(2+3-2,2-1) * (4-3)^binomial(3+3-2,3-1) = 3^1 * 2^3 * 1 = 24.

MAPLE

f := (x, p, r)->`if`(r<>0, `if`(p>0, product((x-m+1)^binomial(m+r-2, m-1), 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

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Last modified December 10 00:54 EST 2019. Contains 329885 sequences. (Running on oeis4.)