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A108075
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Triangle in A071945 with rows reversed.
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0
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1, 1, 1, 3, 3, 1, 9, 9, 5, 1, 31, 31, 19, 7, 1, 113, 113, 73, 33, 9, 1, 431, 431, 287, 143, 51, 11, 1, 1697, 1697, 1153, 609, 249, 73, 13, 1, 6847, 6847, 4719, 2591, 1151, 399, 99, 15, 1, 28161, 28161, 19617, 11073, 5201, 2001, 601, 129, 17, 1, 117631, 117631, 82623
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| D. Baccherini, D. Merlini and R. Sprugnoli, Level generating trees and proper Riordan arrays, Applicable Analysis and Discrete Mathematics, 2, 2008, 69-91 (see p. 88). [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 21 2008]
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FORMULA
| G.f.=(1-q)/[z(1+z)(2-t+tq)], where q=sqrt(1-4z-4z^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 06 2005
T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n,k+1), T(0,0)=1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2009]
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EXAMPLE
| 1; 1,1; 3,3,1; 9,9,5,1; 31,31,19,7,1; ...
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MAPLE
| q:=sqrt(1-4*z-4*z^2): G:=(1-q)/z/(1+z)/(2-t+t*q): Gser:=simplify(series(G, z=0, 13)): P[0]:=1: for n from 1 to 10 do P[n]:=coeff(Gser, z^n) od: for n from 0 to 10 do seq(coeff(t*P[n], t^k), k=1..n+1) od; # yields sequence in triangular form (Deutsch)
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CROSSREFS
| Row sums yield A052705. Column 0 yields A052709.
Sequence in context: A078033 A193741 A193824 * A084145 A122919 A188513
Adjacent sequences: A108072 A108073 A108074 * A108076 A108077 A108078
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 05 2005
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 06 2005
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