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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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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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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.
Adjacent sequences: A006855 A006856 A006857 this_sequence A006859 A006860 A006861
Sequence in context: A107935 A008451 A033276 this_sequence A027818 A054149 A025607
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KEYWORD
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nonn,easy
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AUTHOR
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Simon Plouffe, njas
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EXTENSIONS
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Edited by njas, Oct 20 2007
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