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A025226
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a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 2. Also a(n) = 3^n*C(n-1), where C = A000108 (Catalan numbers). E.g. a(3)=3^3*C(2)=27*2=54.
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2
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3, 9, 54, 405, 3402, 30618, 288684, 2814669, 28146690, 287096238, 2975361012, 31241290626, 331638315876, 3553267670100, 38375290837080, 417331287853245, 4566095267100210
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| G.f.: (1-sqrt(1-12*x))/2 - Michael Somos, Jun 08, 2000.
Given g.f. C(x) and given A(x)= g.f. of A100239, then B(x)=A(x)-1-2x satisfies B(x)=x-C(x*B(x)). - Michael Somos Sep 07 2005
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MATHEMATICA
| Rest[CoefficientList[Series[(1-Sqrt[1-12x])/2, {x, 0, 20}], x]] (* From Harvey P. Dale, Mar 09 2011 *)
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PROG
| (PARI) a(n)=polcoeff((1-sqrt(1-12*x+x*O(x^n)))/2, n)
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CROSSREFS
| Cf. A000108, A005159.
Sequence in context: A077795 A038496 A175596 * A001194 A032179 A175117
Adjacent sequences: A025223 A025224 A025225 * A025227 A025228 A025229
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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