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Search: id:A006858
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| A006858 |
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G.f.: x(1+x)(1+6x+x^2)/(1-x)^7.
(Formerly M4935)
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+0
6
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| 0, 1, 14, 84, 330, 1001, 2548, 5712, 11628, 21945, 38962, 65780, 106470, 166257, 251720, 371008, 534072, 752913, 1041846, 1417780, 1900514, 2513049, 3281916, 4237520, 5414500, 6852105, 8594586, 10691604, 13198654, 16177505, 19696656
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Arises in enumerating paths in the plane.
a(n+1) is the determinant of the n-by-n Hankel matrix whose first row is the Catalan numbers C_n (A000108) beginning at C_4 = 14. Example (n=3): det[{{14, 42, 132}, {42, 132, 429}, {132, 429, 1430}}] = 330. - David Callan (callan(AT)stat.wisc.edu), Mar 30 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).
G. Kreweras and H. Niederhausen, Solution of an enumerative problem connected with lattice paths, European J. Combin., 2 (1981), 55-60.
J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.2(ii), case a=1]
Stanley, R. P., Enumerative Combinatorics, Volume 1 (1986), p. 221, Example 4.5.18.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
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a(n) = (n+1)*binomial(2n+4, 5)/12 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 06 2004
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MAPLE
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series((x+7*x^2+7*x^3+x^4)/(1-x)^7, x, 50);
b:=binomial; t72b:= proc(a, k) ((a+k+1)/(a+1)) * b(k+2*a+1, k)*b(k+3*a/2+1, k)/(b(k+a/2, k)); end; [seq(t72b(1, k), k=0..40)];
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CROSSREFS
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Cf. A006332.
Sequence in context: A107935 A008451 A033276 this_sequence A027818 A054149 A025607
Adjacent sequences: A006855 A006856 A006857 this_sequence A006859 A006860 A006861
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KEYWORD
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nonn,easy
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AUTHOR
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Simon Plouffe, N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 20 2007
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