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Search: id:A055209
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| A055209 |
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Product_{i=0..n} i!^2. |
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+0
14
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| 1, 1, 4, 144, 82944, 1194393600, 619173642240000, 15728001190723584000000, 25569049282962188245401600000000, 3366980847587422591723894776791040000000000, 44337041641882947649156022595410930014617600000000000000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) is the discriminant of the polynomial x(x+1)(x+2)...(x+n). - Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 13 2003
This is the Hankel transform (see A001906 for definition) of the sequence : 1, 0, 1, 0, 5, 0, 61, 0, 1385, 0, 50521, ... (see A000364: Euler numbers). Philippe DELEHAM, Apr 06 2005
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REFERENCES
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R. Ehrenborg, The Hankel determinant of exponential polynomials, Amer. Math. Monthly, 107 (2000), 557-560.
Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.
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LINKS
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J. W. Layman, The Hankel Transform and Some of its Properties, J. Integer Sequences, 4 (2001), #01.1.5.
Index entries for sequences related to factorial numbers
C. Radoux, Determinants de Hankel et theoreme de Sylvester
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FORMULA
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a(n) = A000178(n)^2. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 06 2004
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MAPLE
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seq(mul(mul(j^2, j=1..k), k=0..n), n=0..10); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 21 2007
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CROSSREFS
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A055209 is the Hankel transform (see A001906 for definition) of A000023, A000142, A000166, A000522, A003701, A010842, A010843, A051295, A052186, A053486, A053487 - John W. Layman (layman(AT)math.vt.edu) and Michael Somos, Jul 27 2000
Sequence in context: A122747 A069135 A138176 this_sequence A030450 A041629 A159197
Adjacent sequences: A055206 A055207 A055208 this_sequence A055210 A055211 A055212
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jul 18 2000
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