A276995 - OEIS

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

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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:

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