A276995 Triangle read by rows, T(n,k) = k^(n-k)*(n-k)!*Sum_{j=0..n-k}(-1)^j/j! for 0<=k<=n.

1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 2, 4, 0, 1, 0, 9, 16, 9, 0, 1, 0, 44, 144, 54, 16, 0, 1, 0, 265, 1408, 729, 128, 25, 0, 1, 0, 1854, 16960, 10692, 2304, 250, 36, 0, 1, 0, 14833, 237312, 193185, 45056, 5625, 432, 49, 0, 1

Offset

0,12

Links

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

Formula

T(n,k) = k^(n-k)*Gamma(1+n-k,-1)/exp(1).

Example

Triangle starts:
1;
0,    1;
0,    0,     1;
0,    1,     0,     1;
0,    2,     4,     0,    1;
0,    9,    16,     9,    0,   1;
0,   44,   144,    54,   16,   0,  1;
0,  265,  1408,   729,  128,  25,  0,  1;
0, 1854, 16960, 10692, 2304, 250, 36,  0,  1;

Maple

T := (n, k) -> A000166(n-k)*k^(n-k): for n from 0 to 9 do seq(T(n, k), k=0..n) od;

Mathematica

Table[If[n-k == 0, 1, k^(n-k) Subfactorial[n-k]], {n, 0, 10}, {k, 0, n}] // Flatten

Crossrefs

Cf. A000166, A277004.

Sequence in context: A348892 A327005 A300858 * A074078 A309635 A130659

Adjacent sequences: A276992 A276993 A276994 * A276996 A276997 A276998

Keyword

nonn,tabl

Author

Peter Luschny, Oct 10 2016

Status

approved