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A244884 Expansion of (-2 +x^2 +x -x*sqrt(1-2*x-3*x^2))/(-1 +x -sqrt(1-2*x-3*x^2)). 2
1, 1, 1, 2, 5, 12, 30, 76, 196, 512, 1353, 3610, 9713, 26324, 71799, 196938, 542895, 1503312, 4179603, 11662902, 32652735, 91695540, 258215664, 728997192, 2062967382, 5850674704, 16626415975, 47337954326, 135015505407, 385719506620 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..200 from Vincenzo Librandi)

J.-L. Baril, A. Petrossian, Equivalence classes of Dyck paths modulo some statistics, 2004.

FORMULA

a(n) ~ 3^(n+1/2)/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jul 10 2014

MATHEMATICA

CoefficientList[Series[(-2 + x^2 + x - x Sqrt[1 - 2 x - 3 x^2])/(-1 + x - Sqrt[1 - 2 x - 3 x^2]), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 10 2014 *)

PROG

(PARI) x='x + O('x^50); Vec((-2 +x^2 +x -x*sqrt(1-2*x-3*x^2))/(-1 +x -sqrt(1-2*x-3*x^2))) \\ G. C. Greubel, Feb 14 2017

CROSSREFS

Apart from initial terms, same as A002026.

Sequence in context: A051450 A038508 A105695 * A002026 A026938 A086622

Adjacent sequences:  A244881 A244882 A244883 * A244885 A244886 A244887

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 09 2014

STATUS

approved

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Last modified February 21 04:22 EST 2018. Contains 299389 sequences. (Running on oeis4.)