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A277004
Triangle read by rows, T(n,k) = k^k*(n-k)!*Sum_{j=0..n-k}(-1)^j/j! for 0<=k<=n.
1
1, 0, 1, 1, 0, 4, 2, 1, 0, 27, 9, 2, 4, 0, 256, 44, 9, 8, 27, 0, 3125, 265, 44, 36, 54, 256, 0, 46656, 1854, 265, 176, 243, 512, 3125, 0, 823543, 14833, 1854, 1060, 1188, 2304, 6250, 46656, 0, 16777216, 133496, 14833, 7416, 7155, 11264, 28125, 93312, 823543, 0, 387420489
OFFSET
0,6
FORMULA
T(n,k) = k^k*Gamma(1+n-k,-1)/exp(1).
EXAMPLE
Triangle starts:
[ 1]
[ 0, 1]
[ 1, 0, 4]
[ 2, 1, 0, 27]
[ 9, 2, 4, 0, 256]
[ 44, 9, 8, 27, 0, 3125]
[ 265, 44, 36, 54, 256, 0, 46656]
[ 1854, 265, 176, 243, 512, 3125, 0, 823543]
[14833, 1854, 1060, 1188, 2304, 6250, 46656, 0, 16777216]
MAPLE
T := (n, k) -> k^k*(n-k)!*add((-1)^j/j!, j=0..n-k): seq(seq(T(n, k), k=0..n), n=0..9);
CROSSREFS
Cf. T(n,0) = T(n+1,1) = A000166(n), T(n,n) = T(n+2,n) = A000312(n), A276995.
Sequence in context: A357586 A266861 A265435 * A371077 A113092 A033324
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Oct 10 2016
STATUS
approved