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 A368298 a(n) is the permanent of the n-th order Hankel matrix of Catalan numbers M(n) whose generic element is given by M(i,j) = A000108(i+j+n) with i,j = 0, ..., n-1. 2
 1, 1, 53, 490614, 930744290905, 386735380538157813864, 36494318768452684668237864399892, 800075179375382235705309991148469060609055210, 4138855242465150993428071754285859188133806122546895149328625, 5109461743591866972924602083859433690113667142460933537037028649653229023827000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..9. Wikipedia, Hankel matrix. EXAMPLE a(3) = 490614: 5, 14, 42; 14, 42, 132; 42, 132, 429. MAPLE with(LinearAlgebra): C:= proc(n) option remember; binomial(2*n, n)/(n+1) end: a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> C(i+j+n-2)))): seq(a(n), n=0..10); # Alois P. Heinz, Dec 20 2023 MATHEMATICA a[n_]:=If[n==0, 1, Permanent[Table[CatalanNumber[i+j+n], {i, 0, n-1}, {j, 0, n-1}]]]; Array[a, 10, 0] CROSSREFS Cf. A000108, A355400. Diagonal of A368025. Sequence in context: A183793 A367766 A336440 * A145332 A087530 A125037 Adjacent sequences: A368295 A368296 A368297 * A368299 A368300 A368301 KEYWORD nonn AUTHOR Stefano Spezia, Dec 20 2023 STATUS approved

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Last modified July 13 08:08 EDT 2024. Contains 374274 sequences. (Running on oeis4.)