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A108430 Number of d steps in all paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1). 1
3, 31, 311, 3151, 32299, 334335, 3488239, 36627487, 386618387, 4098713631, 43611791783, 465496885231, 4981942135611, 53443871159551, 574500093677535, 6186886528903231, 66735614131858723, 720897596248427295 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..18.

Emeric Deutsch, Problem 10658: Another Type of Lattice Path, American Math. Monthly, 107, 2000, 368-370.

FORMULA

a(n) = (1/n)*sum(k*binomial(n,2n-k)*binomial(n+k,n-1), k=n..2n).

EXAMPLE

a(1) = 3 because in the paths ud, Udd we have 3 d steps altogether.

MAPLE

a:=n->(1/n)*sum(k*binomial(n, 2*n-k)*binomial(n+k, n-1), k=n..2*n): seq(a(n), n=1..22);

CROSSREFS

Cf. A027307, A108429.

Sequence in context: A065533 A048550 A236527 * A113075 A111137 A037785

Adjacent sequences:  A108427 A108428 A108429 * A108431 A108432 A108433

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Jun 03 2005

STATUS

approved

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Last modified September 18 12:00 EDT 2019. Contains 327170 sequences. (Running on oeis4.)