

A091063


Triangle, read by rows, such that the initial terms of the binomial transform of the nth row forms the nth row of triangle A059438 transposed (permutations of [1..n] with k components).


2



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, 1, 8, 35, 122, 415, 1540, 6413, 28498, 111866, 0, 1, 9, 44, 168, 609, 2361, 10314, 50382, 257922, 1143554, 0, 1
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OFFSET

0,8


COMMENTS

The main diagonal equals A075834 shift 1 place left; subsequent diagonals of this triangle are selfconvolutions of the main diagonal. A075834 has the property that the nth term of the nth selfconvolution of A075834 equals n!. The first (n+1) terms of the binomial transform of the nth row forms the nth row of triangle A059438 transposed, which has row sums equal to the factorials. A059438 is also formed from the selfconvolutions of its main diagonal (A003319).


LINKS

Table of n, a(n) for n=0..66.


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

Cf. A075834, A059438, A003319.
Sequence in context: A130020 A292870 A306704 * A246935 A342120 A198793
Adjacent sequences: A091060 A091061 A091062 * A091064 A091065 A091066


KEYWORD

nonn,tabl


AUTHOR

Paul D. Hanna, Dec 17 2003


STATUS

approved



