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Search: id:A005587
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| A005587 |
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n(n+5)(n+6)(n+7)/24.
(Formerly M4929)
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+0
5
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| 0, 14, 42, 90, 165, 275, 429, 637, 910, 1260, 1700, 2244, 2907, 3705, 4655, 5775, 7084, 8602, 10350, 12350, 14625, 17199, 20097, 23345, 26970, 31000, 35464, 40392, 45815, 51765, 58275, 65379, 73112, 81510, 90610, 100450, 111069, 122507, 134805, 148005
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) = number of Standard Young Tableaux of shape (n+3,4). - David Callan (callan(AT)stat.wisc.edu), Aug 17 2004
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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).
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 796.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6
Matthew M. Conroy, Home page (listed instead of email address)
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.: (14 - 28x + 20x^2 - 5x^3) / (1 - x)^5.
C(7+n, 4)-C(7+n, 3) - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 09 2005
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MAPLE
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A005587:=z*(-14+28*z-20*z**2+5*z**3)/(z-1)**5; [S. Plouffe in his 1992 dissertation.]
seq(numbperm(n, 4)/24-numbperm(n, 3)/6, n=7..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 20 2008
a:=n->(sum(numbcomp(n, 4), j=9..n)):seq(a(n)/4, n=8..47); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 26 2008]
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CROSSREFS
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Fifth diagonal of Catalan triangle A033184. Fifth column of Catalan triangle A009766.
Numerator polynomial 14 - 28x + 20x^2 - 5x^3 from fourth row of triangle A062991.
Sequence in context: A064512 A118237 A163756 this_sequence A120714 A041378 A041380
Adjacent sequences: A005584 A005585 A005586 this_sequence A005588 A005589 A005590
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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).
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EXTENSIONS
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M4929 (this sequence) and M4930 were the same.
More terms from Matthew Conroy (list1(AT)madandmoonly.com), Jan 16 2006
Plouffe Maple line edited by N. J. A. Sloane (njas(AT)research.att.com), May 13 2008
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