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A005587
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n(n+5)(n+6)(n+7)/24.
(Formerly M4929)
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8
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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;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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a(n) = number of Standard Young Tableaux of shape (n+3,4). - David Callan, Aug 17 2004
a(n) = A214292(n+6,3). - Reinhard Zumkeller, Jul 12 2012
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REFERENCES
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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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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)
_Simon 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.
_Simon 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; [Simon 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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MATHEMATICA
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Table[n (n + 5) (n + 6) (n + 7)/24, {n, 0, 60}] (* From Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)
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PROG
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(MAGMA) [n*(n+5)*(n+6)*(n+7)/24: n in [0..40]]; // Vincenzo Librandi, Mar 20 2013
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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: A208360 A208359 A163756 * A212514 A120714 A041378
Adjacent sequences: A005584 A005585 A005586 * 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.
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EXTENSIONS
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M4929 (this sequence) and M4930 were the same.
More terms from Matthew Conroy, Jan 16 2006
Plouffe Maple line edited by N. J. A. Sloane, May 13 2008
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STATUS
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approved
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