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A262543
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Number of rooted asymmetrical polyenoids of type U_n* having n edges.
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4
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0, 2, 4, 10, 28, 84, 264, 858, 2860, 9724, 33592, 117572, 416024, 1485800, 5348880, 19389690, 70715340, 259289580, 955277400, 3534526380, 13128240840, 48932534040, 182965127280, 686119227300, 2579808294648, 9723892802904, 36734706144304, 139067101832008, 527495903500720
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OFFSET
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1,2
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COMMENTS
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Essentially the same as A068875 and A002420. See those entries for much more information.
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LINKS
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FORMULA
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G.f.: 1 - 2*x - sqrt(1 - 4*x).
G.f.: x*(A(x) - 1), where A(x) is the g.f. of A068875. (End)
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EXAMPLE
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G.f. = 2*x^2 + 4*x^3 + 10*x^4 + 28*x^5 + 84*x^6 + 264*x^7 + 858*x^8 + ...
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MAPLE
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A262543List := proc(m) local A, P, n; A := [0, 2]; P := [2];
for n from 1 to m - 2 do P := ListTools:-PartialSums([op(P), P[-1]]);
A := [op(A), P[-1]] od; A end: A262543List(29); # Peter Luschny, Mar 24 2022
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MATHEMATICA
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Table[If[n==1, 0, 2 CatalanNumber[n-1]], {n, 1, 26}] (* Peter Luschny, Feb 27 2017 *)
Join[{0}, Rest[CoefficientList[Series[2 (1 - Sqrt[1 - 4 x])/(2 x), {x, 0, 30}], x]]] (* Vincenzo Librandi, Feb 28 2017 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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