A110131 Determinant of n X n matrix M_{i,j} = 2^i*P_i(j), where P_i(j) is the Legendre polynomial of order i at j and i and j are 0-based.
1, 2, 24, 2880, 4838400, 146313216000, 97339256340480000, 1683704371913057894400000, 873705178746128941669416960000000, 15414977576506278044562764045746176000000000, 10334857226047177887548812577909403133201612800000000000
Offset: 1
Links
- Muniru A Asiru, Table of n, a(n) for n = 1..36
Programs
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Maple
seq(mul(mul((j+k),j=1..k), k=1..n-1), n=1..9); # Zerinvary Lajos, Sep 21 2007
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PARI
a(n)=my(t=1);prod(k=1,n-1,t*=4*k-2) \\ Charles R Greathouse IV, Oct 25 2011
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PARI
a(n)=matdet(matrix(n,n,i,j,pollegendre(i-1,j-1)<<(i-1))) \\ Charles R Greathouse IV, Oct 25 2011
Formula
a(n) = 2^n * Product_{k=1..n} (2*k-1)!/(k-1)!.
a(n) = 2^n * A086205(n).
From Alois P. Heinz, Jun 30 2022: (Start)
a(n) = Product_{i=1..n-1} Product_{j=i..n-1} (i+j).
a(n) = A112332(n). (End)