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A278991 a(n) is the number of simple linear diagrams with n+1 chords. 1
0, 1, 3, 24, 211, 2325, 30198, 452809, 7695777, 146193678, 3069668575, 70595504859, 1764755571192, 47645601726541, 1381657584006399, 42829752879449400, 1413337528735664887, 49465522112961344241, 1830184115528550306438, 71375848864779552073957 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 0..301

E. Krasko, A. Omelchenko, Enumeration of Chord Diagrams without Loops and Parallel Chords, arXiv preprint arXiv:1601.05073 [math.CO], 2016.

E. Krasko, A. Omelchenko, Enumeration of Chord Diagrams without Loops and Parallel Chords, The Electronic Journal of Combinatorics, 24(3) (2017), #P3.43.

FORMULA

E.g.f.: (1-sqrt(1-2*x))*(1-2*x)^(-3/2)*exp(-1-x+sqrt(1-2*x)).

a(n) ~ 2^(n+3/2) * n^(n+1) / exp(n+3/2). - Vaclav Kotesovec, Dec 07 2016

a(n) = (2*n-1)*a(n-1) + (4*n-3)*a(n-2) + (2*n-4)*a(n-3). - Gheorghe Coserea, Dec 10 2016

MATHEMATICA

a[0] = 0; a[1] = 1; a[2] = 3; a[n_] := a[n] = (2 n - 1) a[n - 1] + (4 n - 3) a[n - 2] + (2 n - 4) a[n - 3]; Table[a@ n, {n, 0, 19}] (* Michael De Vlieger, Dec 10 2016 *)

PROG

(PARI)

seq(N) = {

  my(a = vector(N)); a[1]=1; a[2]=3; a[3]=24;

  for (n=4, N, a[n] = (2*n-1)*a[n-1] + (4*n-3)*a[n-2] + (2*n-4)*a[n-3]);

  concat(0, a);

};

seq(20) \\ Gheorghe Coserea, Dec 10 2016

(PARI)

N = 20; x = 'x + O('x^N);

concat(0, Vec(serlaplace((1-sqrt(1-2*x))*(1-2*x)^(-3/2)*exp(-1-x+sqrt(1-2*x))))) \\ Gheorghe Coserea, Dec 10 2016

CROSSREFS

Sequence in context: A063979 A308354 A073978 * A232692 A000279 A292311

Adjacent sequences:  A278988 A278989 A278990 * A278992 A278993 A278994

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 07 2016

EXTENSIONS

Offset corrected by Gheorghe Coserea, Dec 10 2016

STATUS

approved

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Last modified October 15 23:54 EDT 2019. Contains 328038 sequences. (Running on oeis4.)