A145118 Denominator polynomials for continued fraction generating function for n!.

1, 1, 1, -1, 1, -2, 1, -4, 2, 1, -6, 6, 1, -9, 18, -6, 1, -12, 36, -24, 1, -16, 72, -96, 24, 1, -20, 120, -240, 120, 1, -25, 200, -600, 600, -120, 1, -30, 300, -1200, 1800, -720, 1, -36, 450, -2400, 5400, -4320, 720, 1, -42, 630, -4200, 12600, -15120

Offset: 0

Author

Paul Barry, Oct 02 2008

Keywords

• easy
• sign
• tabf

Comments

Row sums are A056920. T(n,1) gives quarter squares A002620. T(n,2) appears to coincide with 2*A000241(n+1).

Examples

			Triangle begins:
1;
1;
1,  -1;
1,  -2;
1,  -4,   2;
1,  -6,   6;
1,  -9,  18,    -6;
1, -12,  36,   -24;
1, -16,  72,   -96,   24;
1, -20, 120,  -240,  120;
1, -25, 200,  -600,  600,  -120;
1, -30, 300, -1200, 1800,  -720;
1, -36, 450, -2400, 5400, -4320, 720;
		

Links

• Alois P. Heinz, Rows n = 0..200, flattened

Crossrefs

Cf. A021010, A008297, A066667, A105278.

Programs

Maple

T:= (n, k)-> (-1)^k* binomial(iquo(n+1, 2),k) *binomial(iquo(n, 2), k)*k!:
seq (seq (T(n, k), k=0..iquo(n, 2)), n=0..16);  # Alois P. Heinz, Dec 04 2012

Formula

T(n,k) = (-1)^k C(floor((n+1)/2),k) * C(floor(n/2),k)*k!.