OFFSET
0,8
COMMENTS
The main diagonal equals A075834 shift 1 place left; subsequent diagonals of this triangle are self-convolutions of the main diagonal. A075834 has the property that the n-th term of the n-th self-convolution of A075834 equals n!. The first (n+1) terms of the binomial transform of the n-th row forms the n-th row of triangle A059438 transposed, which has row sums equal to the factorials. A059438 is also formed from the self-convolutions of its main diagonal (A003319).
EXAMPLE
Rows begin:
{1},
{1,0},
{1,1,0},
{1,2,2,0},
{1,3,5,7,0},
{1,4,9,18,34,0},
{1,5,14,34,86,206,0},
{1,6,20,56,162,508,1476,0},
{1,7,27,85,269,939,3549,12123,0},...
Initial terms of the binomial transform of each row forms A059438:
{1},
{1,1},
{1,2,3},
{1,3,7,13},
{1,4,12,32,71},
{1,5,18,58,177,461},
{1,6,25,92,327,1142,3447},
{1,7,33,135,531,2109,8411,29093},
{1,8,42,188,800,3440,15366,69692,273343},...
which has row sums equal to the factorials.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Dec 17 2003
STATUS
approved