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Search: id:A003161
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| A003161 |
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A binomial coefficient sum.
(Formerly M1931)
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+0
5
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| 1, 1, 2, 9, 36, 190, 980, 5705, 33040, 204876, 1268568, 8209278, 53105976, 354331692, 2364239592, 16140234825, 110206067400, 765868074400, 5323547715200, 37525317999884, 264576141331216, 1886768082651816
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The number of triples of standard tableaux of the same shape of height less than or equal to 2. - Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Mar 29 2007
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Problem E2384, Amer. Math. Monthly, 81 (1974), 170-171.
F. Bergeron, L. Favreau and D. Krob, Conjectures on the enumeration of tableaux of bounded height, Discrete Math, vol. 139, no. 1-3 (1995), 463-468.
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FORMULA
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a(n)=Sum_{k, 0=k<=n}A120730(n,k)^3 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2008]
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PROGRAM
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(PARI) a(n)=sum(k=0, n\2, (binomial(n, k)-binomial(n, k-1))^3) /* Michael Somos Jun 02 2005 */
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CROSSREFS
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Cf. A003162.
Cf. A001405, A000108, A129123.
Sequence in context: A137955 A150981 A150982 this_sequence A101610 A111601 A037553
Adjacent sequences: A003158 A003159 A003160 this_sequence A003162 A003163 A003164
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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