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Search: id:A068943
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| A068943 |
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a(n) = f(n, n, n), where f is the generalized super falling factorial (see comments for definition.). |
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4
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| 1, 2, 24, 331776, 2524286414780230533120, 18356962141505758798331790171539976807981714702571497465907439808868887035904000000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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).
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FORMULA
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a(n) = Product_{m = 1..n} (n-m+1)^binomial(m+n-2, m-1)
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EXAMPLE
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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.
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MAPLE
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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);
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CROSSREFS
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Sequence in context: A098679 A123851 A120122 this_sequence A100815 A100010 A045510
Adjacent sequences: A068940 A068941 A068942 this_sequence A068944 A068945 A068946
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KEYWORD
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easy,nonn
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AUTHOR
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Francois Jooste (phukraut(AT)hotmail.com), Mar 09 2002
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EXTENSIONS
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Edited by David Wasserman (dwasserm(AT)earthlink.net), Mar 14 2003
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