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

1,2

Links

Muniru A Asiru, Table of n, a(n) for n = 1..36

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)

Maple

seq(mul(mul((j+k), j=1..k), k=1..n-1), n=1..9); # Zerinvary Lajos, Sep 21 2007

Prog

(PARI) a(n)=my(t=1); prod(k=1, n-1, t*=4*k-2) \\ Charles R Greathouse IV, Oct 25 2011
(PARI) a(n)=matdet(matrix(n, n, i, j, pollegendre(i-1, j-1)<<(i-1))) \\ Charles R Greathouse IV, Oct 25 2011

Crossrefs

Cf. A000079, A086205, A112332.

Sequence in context: A240993 A007079 A083697 * A112332 A101339 A111428

Adjacent sequences: A110128 A110129 A110130 * A110132 A110133 A110134

Keyword

easy,nonn

Author

Paul Barry, Jul 13 2005

Status

approved