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Search: id:A122871
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| A122871 |
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Expansion of (1-2x-sqrt(1-4x-8x^2))/(6x^2). |
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+0
1
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| 1, 2, 7, 26, 106, 452, 1999, 9074, 42046, 198044, 945430, 4564100, 22243060, 109285256, 540738943, 2692103714, 13475973238, 67784600108, 342439638418, 1736727343436, 8839203054604, 45132514680248, 231121351433158
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Series reversion of x/(1+2x+3x^2). Binomial transform is A107264. Counts colored Motzkin paths. Second binomial transform of 1,0,3,0,18,0... or 3^n*C(n) (A005159) with interpolated zeros.
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FORMULA
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E.g.f.: exp(2x)Bessel_I(1, sqrt(3)*2*x)/(sqrt(3)x); a(n)=sum{k=0..floor(n/2), C(n,2k)C(k)3^k*2^(n-2k)};
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CROSSREFS
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Adjacent sequences: A122868 A122869 A122870 this_sequence A122872 A122873 A122874
Sequence in context: A119243 A141370 A052706 this_sequence A000151 A102319 A006603
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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 16 2006
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