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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
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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.
Hankel transform is 3^C(n+1,2). [From Paul Barry (pbarry(AT)wit.ie), Oct 01 2009]
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FORMULA
| 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)};
G.f.: 1/(1-2x-3x^2/(1-2x-3x^2/(1-2x-3x^2/(1-2x-3x^2/(1-.... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Oct 01 2009]
Conjecture: (n+2)*a(n) -2*(2n+1)*a(n-1) +8*(1-n)*a(n-2)=0. - R. J. Mathar, Nov 14 2011
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CROSSREFS
| Sequence in context: A150559 A150560 A150561 * A150562 A150563 A150564
Adjacent sequences: A122868 A122869 A122870 * A122872 A122873 A122874
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 16 2006
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