OFFSET
1,1
COMMENTS
Row sums are:
{2, 14, 112, 1008, 10080, 110880, 1330560, 17297280, 242161920, 3632428800,...}.
The division by 6! and changing the first element gives a nicer looking result.
FORMULA
A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (n + 4)*(n + 3)*A(n - 2, k - 1).
EXAMPLE
{2},
{7, 7},
{1, 110, 1},
{1, 503, 503, 1},
{1, 576, 8926, 576, 1},
{1, 667, 54772, 54772, 667, 1},
{1, 778, 118799, 1091404, 118799, 778, 1},
{1, 911, 207621, 8440107, 8440107, 207621, 911, 1},
{1, 1068, 329900, 27180372, 187139238, 27180372, 329900, 1068, 1},
{1, 1251, 496770, 65297294, 1750419084, 1750419084, 65297294, 496770, 1251, 1}
MATHEMATICA
Clear[A] A[1, 1] = 2*6!/720; A[2, 1] := A[2, 2] = 7!/720;
A[3, 2] = (2*8! - 2*6!)/720; A[4, 2] = A[4, 3] = ( 9! - 6!)/720;
A[n_, 1] := 6!/720; A[n_, n_] := 6!/720;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n + 4)*(n + 3)*A[n - 2, k - 1];
a = Table[A[n, k], {n, 10}, {k, n}];
Flatten[a]
Table[Apply[Plus, a[[n]]], {n, 1, 10}];
Table[Apply[Plus, 720*a[[n]]]/(2*(n + 5)!), {n, 1, 10}];
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Dec 31 2008
STATUS
approved