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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).
3
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
0,3
FORMULA
A198061(n,2) = A006127(n+1)
EXAMPLE
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
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 *)
CROSSREFS
Cf. A198060.
Sequence in context: A060155 A209127 A127954 * A265583 A339754 A238156
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Nov 02 2011
STATUS
approved