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Search: id:A098430
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| 1, 8, 96, 1280, 17920, 258048, 3784704, 56229888, 843448320, 12745441280, 193730707456, 2958796259328, 45368209309696, 697972450918400, 10768717814169600, 166556168859156480, 2581620617316925440
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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4^n binom[2n,n] counts walks of 2n steps North, East, South or West that start at the origin and end on the line y=x. For example, a(1)=8 counts EW, EN, NE, NS, WE, WS, SN, SW. If the walk has i East and j North steps, then it must have n-j West and n-i South steps. There are Multinomial[i,j,n-j,n-i] ways to arrange these steps and summing over i and j gives the result. - David Callan (callan(AT)stat.wisc.edu), Oct 11 2005
Hankel transform is A121913. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 01 2009]
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REFERENCES
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Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
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FORMULA
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E.g.f.: exp(8x)BesselI(0, 8x); a(n)=4^n*Binomial(2n, n). a(n)=4^n*A000984(n).
G.f.:1/sqrt(1-16*x) . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 20 2008, corrected R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2009]
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CROSSREFS
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Sequence in context: A066424 A099675 A060458 this_sequence A034177 A052570 A002168
Adjacent sequences: A098427 A098428 A098429 this_sequence A098431 A098432 A098433
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 07 2004
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