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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 (list; table; graph; refs; listen; history; text; internal format)
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: A110324 A266861 A265435 * A113092 A033324 A266145

Adjacent sequences:  A277001 A277002 A277003 * A277005 A277006 A277007

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Oct 10 2016

STATUS

approved

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Last modified January 19 09:51 EST 2021. Contains 340269 sequences. (Running on oeis4.)