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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 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-François 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 July 27 06:56 EDT 2021. Contains 346304 sequences. (Running on oeis4.)