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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
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
Diagonal of A368025.
Sequence in context: A183793 A367766 A336440 * A145332 A087530 A125037
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.)