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Search: id:A098444
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| A098444 |
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Expansion of 1/sqrt(1-6x-11x^2). |
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+0
2
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| 1, 3, 19, 117, 771, 5193, 35629, 247467, 1734931, 12250953, 87006249, 620818047, 4447016781, 31959556983, 230331965379, 1664043517557, 12047551338771, 87387014213433, 634918255153369, 4619923954541247, 33661450900419001
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A084770. Second binomial transform of A098264. Binomial transform is A098443.
Coefficient of x^n in (1 + 3 x + 5 x^2)^n = number of paths from the origin to (n,0) with steps U=(1,1), H=(1,0) and D=(1,-1); U can have 5 colors and H can have 3 colors. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Jan 28 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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E.g.f.: exp(3x)BesselI(0, 2sqrt(5)x)
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CROSSREFS
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Sequence in context: A037585 A084133 A005667 this_sequence A139176 A126809 A020073
Adjacent sequences: A098441 A098442 A098443 this_sequence A098445 A098446 A098447
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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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