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A336945 a(n) = binomial(3*n,n)/(2*n + 1) - 2*binomial(3*(n - 1),n - 1)/(2*n - 1) for n > 0 with a(0) = 1. 0
1, -1, 1, 6, 31, 163, 882, 4896, 27759, 160149, 937365, 5553210, 33237828, 200696356, 1221105376, 7479222624, 46079243631, 285373035417, 1775569951995, 11093660204970, 69574265317095, 437832231422355, 2763889941603630, 17497374053053440, 111061430519553540, 706647507156148428, 4506221447451530172 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..26.

FORMULA

a(n) = if(n == 0, 1, A001764(n) - 2*A001764(n-1)).

O.g.f.: (1 - 2*z)*2*sin(arcsin(sqrt(27*z)/2)/3)/sqrt(3*z). [This is due to Emeric Deutsch.]

MAPLE

# Recurrence:

a := proc(n) option remember; if n < 4 then return [1, -1, 1, 6][n+1] fi;

-((-108*n^2 + 756*n - 1320)*a(n - 3) + (124*n^2 - 520*n + 468)*a(n - 2) + (-43*n^2 + 67*n - 18)*a(n - 1)) / (4*n^2 + 2*n) end:

seq(a(n), n=0..26); # Peter Luschny, Aug 09 2020

MATHEMATICA

a[n_] := Binomial[3*n, n]/(2*n + 1) - 2 * Binomial[3*(n - 1), n - 1]/(2*n - 1); Array[a, 27, 0] (* Amiram Eldar, Aug 08 2020 *)

PROG

(PARI) a(n) = if (n!=0, binomial(3*n, n)/(2*n + 1) - 2*binomial(3*(n - 1), n - 1)/(2*n - 1), 1); \\ Michel Marcus, Aug 09 2020

CROSSREFS

Cf. A001764.

Sequence in context: A003128 A058146 A015449 * A162475 A343350 A036729

Adjacent sequences:  A336942 A336943 A336944 * A336946 A336947 A336948

KEYWORD

sign

AUTHOR

Petros Hadjicostas, Aug 08 2020

STATUS

approved

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Last modified July 28 17:15 EDT 2021. Contains 346335 sequences. (Running on oeis4.)