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A368021
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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+3) with i,j = 0, ..., n-1.
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7
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1, 5, 406, 490614, 8755482505, 2318987094804471, 9179129956137993425772, 546580120389987275414413168012, 492460174883711250780962744103403975159, 6747075036368337341936435881321217868978170152215, 1411689504898999110533224343869931312130954127737962059963934
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OFFSET
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0,2
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LINKS
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FORMULA
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Det(M(n)) = A000330(n+1) (see Mays and Wojciechowski, 2000).
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EXAMPLE
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a(4) = 8755482505:
5, 14, 42, 132;
14, 42, 132, 429;
42, 132, 429, 1430;
132, 429, 1430, 4862.
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MATHEMATICA
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Join[{1}, Table[Permanent[Table[CatalanNumber[i+j+3], {i, 0, n-1}, {j, 0, n-1}]], {n, 10}]]
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PROG
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(PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108
a(n) = matpermanent(matrix(n, n, i, j, C(i+j+1))); \\ Michel Marcus, Dec 11 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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