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Search: id:A098329
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| A098329 |
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Expansion of 1/(1-2x-31x^2)^(1/2). |
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+0
2
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| 1, 1, 17, 49, 481, 2081, 16241, 85457, 600769, 3489601, 23391697, 143000177, 938797729, 5897385313, 38397492017, 244866166289, 1590355308929, 10231490804353, 66456634775441, 429898281869489, 2795449543782241
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Central coefficient of (1+x+8x^2)^n. 7th binomial transform of 2^n*LegendreP(n,-3) (signed version of A084773).
Also number of paths from (0,0) to (n,0) using steps U=(1,1), H=(1,0) and D=(1,-1), the U steps can have 8 colors. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Mar 31 2008
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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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a(n)=sum{k=0..floor(n/2), binomial(n-k, k)binomial(n, k)8^k}.
E.g.f. : exp(x)BesselI(0, 4sqrt(2)x)
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CROSSREFS
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Cf. A084603.
Adjacent sequences: A098326 A098327 A098328 this_sequence A098330 A098331 A098332
Sequence in context: A146706 A120612 A146461 this_sequence A003124 A005570 A146673
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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 03 2004
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