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A088662 Number of peaks at even level in all symmetric Dyck paths of semilength n+2. 1
1, 2, 7, 12, 34, 60, 155, 280, 686, 1260, 2982, 5544, 12804, 24024, 54483, 102960, 230230, 437580, 967538, 1847560, 4047836, 7759752, 16871582, 32449872, 70100044, 135207800, 290473900, 561632400, 1200823560, 2326762800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..29.

FORMULA

G.f.: (1-2z+4z^3)/[2z^2*(1-2z)sqrt(1-4z^2)]-1/(2z^2).

a(2n) = (2n)!(2n^2+4n+1)/[n!(n+1)!], a(2n+1) = 2(2n+1)!/(n!)^2.

a(2n+1) = 2*A002457(n).

a(n) = (n!/4)*((1+(-1)^n)*(n^2+4*n+2)/((n/2)!*(n/2+1)!)+4*(1-(-1)^n)/(n/2-1/2)!^2). - Wesley Ivan Hurt, Jun 23 2015

MAPLE

A088662:=n->(n!/4)*((1+(-1)^n)*(n^2+4*n+2)/((n/2)!*(n/2+1)!)+4*(1-(-1)^n)/(n/2-1/2)!^2): seq(A088662(n), n=0..40); # Wesley Ivan Hurt, Jun 23 2015

MATHEMATICA

Table[(n!/4) ((1 + (-1)^n) (n^2 + 4 n + 2)/((n/2)! (n/2 + 1)!) + 4 (1 - (-1)^n)/(n/2 - 1/2)!^2), {n, 0, 40}] (* Wesley Ivan Hurt, Jun 23 2015 *)

CROSSREFS

Cf. A002457.

Sequence in context: A308706 A059053 A032025 * A073710 A326026 A092831

Adjacent sequences:  A088659 A088660 A088661 * A088663 A088664 A088665

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Nov 21 2003

STATUS

approved

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Last modified October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)