A198061 Array read by antidiagonals, m>=0, n>=0, A(m,n) = sum{k=0..n} sum{j=0..m} sum{i=0..m} (-1)^(j+i)*C(i,j)*n^j*k^(m-j).

1, 0, 2, 0, 2, 3, 0, 2, 6, 4, 0, 2, 11, 12, 5, 0, 2, 20, 32, 20, 6, 0, 2, 37, 84, 70, 30, 7, 0, 2, 70, 224, 240, 130, 42, 8, 0, 2, 135, 612, 834, 550, 217, 56, 9, 0, 2, 264, 1712, 2968, 2354, 1092, 336, 72, 10, 0, 2, 521, 4884, 10826, 10310, 5551, 1960, 492

Offset: 0

Author

Peter Luschny, Nov 02 2011

Keywords

• nonn
• tabl

Examples

			m\n  [0] [1]  [2]   [3]    [4]     [5]    [6]
----------------------------------------------
[0]   1   2    3     4      5       6       7    A000027
[1]   0   2    6    12     20      30      42    A002378
[2]   0   2   11    32     70     130     217    A033994
[3]   0   2   20    84    240     550    1092    A098077
[4]   0   2   37   224    834    2354    5551
[5]   0   2   70   612   2968   10310   28854
		

Crossrefs

Cf. A198060.

Programs

Maple

A198061 := proc(m, n) local i,j,k,pow;
pow := (a,b) -> if a=0 and b=0 then 1 else a^b fi;
add(add(add((-1)^(j+i)*binomial(i,j)*pow(n,j)*pow(k,m-j),i=0..m),j=0..m),k=0..n) end:
for m from 0 to 8 do lprint(seq(A198061(m,n), n=0..6)) od;

Mathematica

Unprotect[Power]; 0^0 = 1; Protect[Power]; a[m_, n_] :=  Sum[(-1)^(j+i)*Binomial[i, j]*n^j*k^(m-j) , {i, 0, m}, {j, 0, m}, {k, 0, n}]; Table[a[m-n, n], {m, 0, 10}, {n, 0, m}] // Flatten (* Jean-François Alcover, Jul 26 2013 *)

Formula

A198061(n,2) = A006127(n+1)