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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.

%I A110131 #32 Jun 30 2022 19:12:18
%S A110131 1,2,24,2880,4838400,146313216000,97339256340480000,
%T A110131 1683704371913057894400000,873705178746128941669416960000000,
%U A110131 15414977576506278044562764045746176000000000,10334857226047177887548812577909403133201612800000000000
%N 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.
%H A110131 Muniru A Asiru, <a href="/A110131/b110131.txt">Table of n, a(n) for n = 1..36</a>
%F A110131 a(n) = 2^n * Product_{k=1..n} (2*k-1)!/(k-1)!.
%F A110131 a(n) = 2^n * A086205(n).
%F A110131 From _Alois P. Heinz_, Jun 30 2022: (Start)
%F A110131 a(n) = Product_{i=1..n-1} Product_{j=i..n-1} (i+j).
%F A110131 a(n) = A112332(n). (End)
%p A110131 seq(mul(mul((j+k),j=1..k), k=1..n-1), n=1..9); # _Zerinvary Lajos_, Sep 21 2007
%o A110131 (PARI) a(n)=my(t=1);prod(k=1,n-1,t*=4*k-2) \\ _Charles R Greathouse IV_, Oct 25 2011
%o A110131 (PARI) a(n)=matdet(matrix(n,n,i,j,pollegendre(i-1,j-1)<<(i-1))) \\ _Charles R Greathouse IV_, Oct 25 2011
%Y A110131 Cf. A000079, A086205, A112332.
%K A110131 easy,nonn
%O A110131 1,2
%A A110131 _Paul Barry_, Jul 13 2005