A104417 Triangle, read by rows, equal to the matrix inverse of A104416, where A104416(n,k) = A008275(k+1,n-k+1) (Stirling numbers of the first kind).

1, 1, 1, 3, 3, 1, 16, 16, 6, 1, 127, 127, 49, 10, 1, 1363, 1363, 531, 115, 15, 1, 18628, 18628, 7286, 1615, 230, 21, 1, 311250, 311250, 121964, 27321, 4040, 413, 28, 1, 6173791, 6173791, 2421471, 545311, 82131, 8841, 686, 36, 1, 142190703, 142190703

Offset

0,4

Comments

Column 0 and column 1 contain A082161.

Links

Table of n, a(n) for n=0..46.

Example

Column 0 forms A082161 that satisfies:
1 = (1-x) + 1*x*(1-x)(1-2x) + 3*x^2*(1-x)(1-2x)(1-3x) +
+ 16*x^3*(1-x)(1-2x)(1-3x)(1-4x) + ...
+ A082161(n+1)*x^n*(1-x)(1-2x)(1-3x)*..*(1-(n+1)*x) + ...
this g.f. can be derived from the matrix inverse, A104416.
Rows begin:
1;
1,1;
3,3,1;
16,16,6,1;
127,127,49,10,1;
1363,1363,531,115,15,1;
18628,18628,7286,1615,230,21,1;
311250,311250,121964,27321,4040,413,28,1; ...

Prog

(PARI)

Crossrefs

Cf. A104416, A082161.

Sequence in context: A239895 A106210 A033842 * A121438 A108391 A111840

Adjacent sequences: A104414 A104415 A104416 * A104418 A104419 A104420

Keyword

nonn,tabl

Author

Paul D. Hanna, Mar 06 2005

Status

approved