OFFSET
0,3
COMMENTS
LINKS
Alois P. Heinz, Rows n = 0..250, flattened
FORMULA
T(n,k) = Sum_{j=k..floor(n/3)}(-1)^(k+j) * C(j,k) * C(n-2j,j) * Bell(n-3j).
EXAMPLE
T(4,1) = 2 because we have 123-4 and 1-234.
Triangle starts:
1;
1;
2;
4, 1;
13, 2;
46, 6;
184, 18, 1;
MAPLE
with(combinat): q := 3: a := proc (n, k) options operator, arrow: sum((-1)^(k+j)*binomial(j, k)*binomial(n+j-j*q, j)*bell(n-j*q), j = k .. floor(n/q)) end proc: for n from 0 to 15 do seq(a(n, k), k = 0 .. floor(n/q)) end do; # yields sequence in triangular form
MATHEMATICA
q = 3; a[n_, k_] := Sum[(-1)^(k+j)*Binomial[j, k]*Binomial[n+j-j*q, j]* BellB[n-j*q], {j, k, Floor[n/q]}]; Table[a[n, k], {n, 0, 15}, {k, 0, Floor[n/q]}] // Flatten (* Jean-François Alcover, Feb 22 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Feb 09 2011
STATUS
approved