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 A122851 Number triangle T(n,k) = C(k,n-k)*(n-k)!. 1
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 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 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 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

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Last modified August 6 15:42 EDT 2020. Contains 336253 sequences. (Running on oeis4.)