

A243413


Number of Dyck paths of semilength n having exactly 1 occurrence of the consecutive steps UDUUDU (with U=(1,1), D=(1,1)).


2



1, 5, 19, 70, 259, 962, 3585, 13399, 50201, 188481, 709001, 2671624, 10082895, 38107919, 144214978, 546413880, 2072553851, 7869081412, 29904874545, 113744129791, 432969825404, 1649313815911, 6287005845873, 23980562901849, 91523321091182, 349497990760012
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OFFSET

4,2


LINKS



FORMULA

a(n) ~ c * d^n / sqrt(n), where d = 3.8821590268628506747194368909643384... (same as for A243412) is the root of the equation d^8  2*d^7  10*d^6 + 12*d^5  5*d^4  2*d^3  5*d^2  8*d  3 = 0, and c = 0.0159763870992602878106411532836296... .  Vaclav Kotesovec, Jun 05 2014


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



