0,8

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).

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.

Cf. A075834, A059438, A003319.

Adjacent sequences: A091060 A091061 A091062 this_sequence A091064 A091065 A091066

Sequence in context: A086460 A136431 A130020 this_sequence A085388 A124540 A124550

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Dec 17 2003