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A145118 Denominator polynomials for continued fraction generating function for n!. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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;

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

CROSSREFS

Cf. A021010, A008297, A066667, A105278.

Sequence in context: A087738 A133113 A124840 * A124927 A126279 A135837

Adjacent sequences:  A145115 A145116 A145117 * A145119 A145120 A145121

KEYWORD

easy,sign,tabf

AUTHOR

Paul Barry, Oct 02 2008

STATUS

approved

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Last modified September 20 02:19 EDT 2021. Contains 347577 sequences. (Running on oeis4.)