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A182959
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G.f. 2*(1+x)^2/(1-2*x+sqrt(1-8*x)).
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1
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1, 5, 20, 96, 528, 3136, 19584, 126720, 841984, 5710848, 39376896, 275185664, 1944821760, 13875707904, 99807723520, 722997411840, 5269761884160, 38620004352000, 284405842575360, 2103530005463040, 15619068033761280
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..20.
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FORMULA
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Let F(x) be the g.f. of A182960, then g.f. of this sequence satisfies:
* A(x) = F(x/A(x)^3) and A(x*F(x)^3) = F(x);
* A(x) = [x/Series_Reversion( x*F(x)^3 )]^(1/3).
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EXAMPLE
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G.f.: A(x) = 1 + 5*x + 20*x^2 + 96*x^3 + 528*x^4 + 3136*x^5 +...
where A(x*F(x)^3) = F(x) is the g.f. of A182960:
F(x) = 1 + 5*x + 95*x^2 + 2496*x^3 + 76063*x^4 + 2524161*x^5 +...
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MATHEMATICA
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CoefficientList[ Series[2 (1 + x)^2/(1 - 2 x + Sqrt[1 - 8 x]), {x, 0, 20}], x] [From Robert G. Wilson v, Dec 31 2010]
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PROG
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(PARI) {a(n)=polcoeff(2*(1+x)^2/(1-2*x+sqrt(1-8*x+x*O(x^n))), n)}
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CROSSREFS
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Cf. A182960.
Sequence in context: A017966 A196532 A002745 * A224661 A020046 A026118
Adjacent sequences: A182956 A182957 A182958 * A182960 A182961 A182962
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Dec 31 2010
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STATUS
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approved
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