A198061 - OEIS

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).

%I #8 Jul 26 2013 03:28:15

%S 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,

%T 70,224,240,130,42,8,0,2,135,612,834,550,217,56,9,0,2,264,1712,2968,

%U 2354,1092,336,72,10,0,2,521,4884,10826,10310,5551,1960,492

%N 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).

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

%e m\n [0] [1] [2] [3] [4] [5] [6]

%e ----------------------------------------------

%e [0] 1 2 3 4 5 6 7 A000027

%e [1] 0 2 6 12 20 30 42 A002378

%e [2] 0 2 11 32 70 130 217 A033994

%e [3] 0 2 20 84 240 550 1092 A098077

%e [4] 0 2 37 224 834 2354 5551

%e [5] 0 2 70 612 2968 10310 28854

%p A198061 := proc(m, n) local i,j,k,pow;

%p pow := (a,b) -> if a=0 and b=0 then 1 else a^b fi;

%p 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:

%p for m from 0 to 8 do lprint(seq(A198061(m,n), n=0..6)) od;

%t 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 *)

%Y Cf. A198060.

%K nonn,tabl

%O 0,3

%A _Peter Luschny_, Nov 02 2011