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A050183 T(2n+5,n), array T as in A051168; a count of Lyndon words. 2
0, 1, 4, 15, 55, 200, 728, 2652, 9690, 35530, 130750, 482885, 1789515, 6653325, 24812400, 92798375, 347993910, 1308233790, 4929576600, 18615637950, 70441574000, 267058714626, 1014283603024, 3858687620200, 14702930414900 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..24.

Index entries for sequences related to Lyndon words

FORMULA

From Petros Hadjicostas, Dec 03 2017: (Start)

a(n) = (1/(2*n+5))*Sum_{d|gcd(n,5)} mu(d)*binomial((2*n+5)/d, n/d). (This is a special case of A. Howroyd's formula for double array A051168.)

a(n) = (1/(2*n+5))*(binomial(2*n+5, n) - binomial((2*n/5)+1, n/5)) if 5|n; = (1/(2*n+5))*binomial(2*n+5, n) otherwise.

(End)

PROG

(PARI) a(n) = (1/(2*n+5))*sumdiv(gcd(n, 5), d, moebius(d)*binomial((2*n+5)/d, n/d)); \\ Michel Marcus, Dec 05 2017

CROSSREFS

A diagonal of the square array described in A051168.

Sequence in context: A039717 A220948 A026013 * A094375 A047018 A064813

Adjacent sequences:  A050180 A050181 A050182 * A050184 A050185 A050186

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified February 24 03:21 EST 2018. Contains 299595 sequences. (Running on oeis4.)