A254883 Triangle read by rows, T(n,k) = sum(j=0..2*(n-k), A254882(n-k,j)*k^j /(n-k)!), n>=0, 0<=k<=n.

1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 6, 9, 3, 1, 0, 24, 48, 24, 4, 1, 0, 120, 300, 200, 50, 5, 1, 0, 720, 2160, 1800, 600, 90, 6, 1, 0, 5040, 17640, 17640, 7350, 1470, 147, 7, 1, 0, 40320, 161280, 188160, 94080, 23520, 3136, 224, 8, 1

Offset: 0

Author

Peter Luschny, Feb 10 2015

Keywords

• nonn
• tabl

Examples

			[1]
[0, 1]
[0, 1, 1]
[0, 2, 2, 1]
[0, 6, 9, 3, 1]
[0, 24, 48, 24, 4, 1]
[0, 120, 300, 200, 50, 5, 1]
[0, 720, 2160, 1800, 600, 90, 6, 1]
		

Crossrefs

Cf. A254882.

Programs

Mathematica

Flatten[{1,0,1,Table[{0,Table[Sum[Sum[Abs[StirlingS1[n-k,m+1]] * Abs[StirlingS1[n-k,j-m]],{m,0,j-1}]*k^j/(n-k)!,{j,0,2*(n-k)}],{k,1,n-1}],1},{n,2,10}]}] (* Vaclav Kotesovec, Feb 10 2015 *)

Sage

T = lambda n,k: sum(A254882(n-k,j)*k^j/factorial(n-k) for j in (0..2*(n-k)))
for n in range(6): [T(n,k) for k in (0..n)]