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A268538 a(n) = n-th prime 3-dimensional Catalan number. 2
1, 1, 2, 12, 107, 1178, 14805, 203885, 3002973, 46573347, 752521980, 12571607865, 215925120675, 3796546970232, 68106673339365, 1243210765414512, 23041656826384341 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

"Prime" here is being used it the sense of "primitive" or "irreducible".

LINKS

Table of n, a(n) for n=0..16.

Manuel Wettstein, Trapezoidal Diagrams, Upward Triangulations, and Prime Catalan Numbers, arXiv:1602.07235 [cs.CG], 2016.

FORMULA

Lemma 15 of Wettstein (2016) gives a formula in terms of the 3-dimensional Catalan numbers (A005789).

MAPLE

A005789 := proc(n)

    2*(3*n)!/(n+2)!/(n+1)!/n! ;

end proc:

maxn := 30 :

Cx := add(A005789(i)*x^i, i=0..maxn) ;

d := 3:

for i from 0 to maxn do

    coeftayl(1/Cx^(d*i-1), x=0, i) ;

    %/(1-d*i) ;

    printf("%d, ", %) ;

end do: # R. J. Mathar, Feb 27 2018

MATHEMATICA

A005789[n_] := 2*(3*n)!/(n+2)!/(n+1)!/n!; Maxn = 30; Cx = Sum[A005789[i]* x^i, {i, 0, Maxn}]; d = 3; Reap[For[i = 0, i <= Maxn, i++, sc = SeriesCoefficient[1/Cx^(d*i-1), {x, 0, i}]; Sow[sc/(1-d*i)]]][[2, 1]] (* Jean-Fran├žois Alcover, Mar 24 2018, after R. J. Mathar *)

CROSSREFS

Primitive terms from A000108, A005789.

Sequence in context: A036077 A275765 A184975 * A319291 A265132 A080446

Adjacent sequences:  A268535 A268536 A268537 * A268539 A268540 A268541

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 24 2016

EXTENSIONS

7 more terms. - R. J. Mathar, Feb 27 2018

STATUS

approved

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Last modified September 21 23:55 EDT 2019. Contains 327286 sequences. (Running on oeis4.)