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, 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

Links

Table of n, a(n) for n=0..54.

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

Adjacent sequences: A277001 A277002 A277003 * A277005 A277006 A277007

Keyword

nonn,tabl

Author

Peter Luschny, Oct 10 2016

Status

approved