A122851 - OEIS

A122851

Number triangle T(n,k) = C(k,n-k)*(n-k)!.

1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0, 2, 3, 1, 0, 0, 0, 6, 4, 1, 0, 0, 0, 6, 12, 5, 1, 0, 0, 0, 0, 24, 20, 6, 1, 0, 0, 0, 0, 24, 60, 30, 7, 1, 0, 0, 0, 0, 0, 120, 120, 42, 8, 1, 0, 0, 0, 0, 0, 120, 360, 210, 56, 9, 1

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OFFSET

0,9

COMMENTS

Row sums are A122852.

Triangle T(n,k), read by rows, given by (0,1,-1,0,0,1,-1,0,0,1,-1,0,0,1,...) DELTA (1,0,0,-1,2,0,0,-2,3,0,0,-3,4,...) where DELTA is the operator defined in A084938. - Philippe Deléham, Dec 12 2011

LINKS

Table of n, a(n) for n=0..65.

FORMULA

Number triangle T(n,k)=[k<=n]*k!/(2k-n)!.

T(n,k) = A008279(k,n-k). - Danny Rorabaugh, Apr 23 2015

EXAMPLE

Triangle begins

0, 1,

0, 1, 1,

0, 0, 2, 1,

0, 0, 2, 3, 1,

0, 0, 0, 6, 4, 1,

0, 0, 0, 6, 12, 5, 1,

0, 0, 0, 0, 24, 20, 6, 1

MATHEMATICA

Flatten[Table[Binomial[k, n-k](n-k)!, {n, 0, 10}, {k, 0, n}]] Harvey P. Dale, May 16 2012

PROG

(Magma) /* As triangle: */ [[Binomial(k, n-k)*Factorial(n-k): k in [0..n]]: n in [0.. 7]]; // Vincenzo Librandi, Apr 24 2015

CROSSREFS

Cf. A094587.

Sequence in context: A191400 A168315 A120730 * A064301 A199881 A060701

Adjacent sequences: A122848 A122849 A122850 * A122852 A122853 A122854

KEYWORD

nonn,tabl,easy

AUTHOR

Paul Barry, Sep 14 2006

STATUS

approved