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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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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, December 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
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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: A044007 A064512 A118237 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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njas
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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 njas, May 13 2008
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