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A262543 Number of rooted asymmetrical polyenoids of type U_n* having n edges. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Essentially the same as A068875 and A002420. See those entries for much more information.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

S. J. Cyvin, J. Brunvoll, E. Brendsdal, B. N. Cyvin and E. K. Lloyd, Enumeration of polyene hydrocarbons: a complete mathematical solution, J. Chem. Inf. Comput. Sci., 35 (1995) 743-751.

S. J. Cyvin, J. Brunvoll, E. Brendsdal, B. N. Cyvin and E. K. Lloyd, Enumeration of polyene hydrocarbons: a complete mathematical solution, J. Chem. Inf. Comput. Sci., 35 (1995) 743-751. [Annotated scanned copy]

MATHEMATICA

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 *)

PROG

(MAGMA) [0] cat [2*Catalan(n-1): n in [2..40]]; // Vincenzo Librandi, Feb 28 2017

(PARI) a(n)=if(n>1, 2*binomial(2*n-2, n-1)/n, 0) \\ Charles R Greathouse IV, Feb 28 2017

CROSSREFS

Cf. A068875, A002420.

Sequence in context: A302146 A202135 A068875 * A289709 A192574 A135336

Adjacent sequences:  A262540 A262541 A262542 * A262544 A262545 A262546

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Oct 06 2015

STATUS

approved

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Last modified October 19 13:38 EDT 2018. Contains 316361 sequences. (Running on oeis4.)