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A080893
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Expansion of the exponential series exp( x C(x) ) = exp( ( 1 - sqrt( 1 - 4 x ) )/2 ), where C(x) is the ordinary generating series of the Catalan numbers A000108.
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1
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1, 1, 3, 19, 193, 2721, 49171, 1084483, 28245729, 848456353, 28875761731, 1098127402131, 46150226651233, 2124008553358849, 106246577894593683, 5739439214861417731, 332993721039856822081, 20651350143685984386753
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| E.G.F. Exp[ ( 1 - Sqrt[ 1 - 4 x ] )/2 ] Recurrence: y(n+2) = 2( 2 n + 1 ) y(n+1) + y(n) Recurrence: y(n+1) = sum( binomial(n, k) binomial(2k, k) k! y(n-k), {k, 0, n} )
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MATHEMATICA
| y[x_] := y[x] = 2(2x - 3)y[x - 1] + y[x - 2]; y[0] = 1; y[1] = 1; Table[y[n], {n, 0, 17}]
With[{nn=20}, CoefficientList[Series[Exp[(1-Sqrt[1-4x])/2], {x, 0, nn}], x] Range[0, nn]!] (* From Harvey P. Dale, Oct 30 2011 *)
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CROSSREFS
| Cf. A000108.
Essentially the same as A001517.
Sequence in context: A101481 A155805 A001517 * A028854 A108292 A053554
Adjacent sequences: A080890 A080891 A080892 * A080894 A080895 A080896
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Emanuele Munarini (munarini(AT)mate.polimi.it), Mar 31 2003
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