A064307 Triangle of coefficients of certain numerator polynomials N(n,x).

1, 1, 0, 1, 2, 1, 1, 10, 17, 2, 1, 37, 181, 111, 6, 1, 126, 1530, 2624, 741, 18, 1, 422, 11607, 43940, 34063, 4950, 57, 1, 1422, 83823, 616894, 1013799, 412698, 33337, 186, 1, 4853, 593203, 7846573, 23794925

Offset: 1

Author

Wolfdieter Lang, Sep 13 2001

Keywords

• nonn
• tabl

Comments

The g.f. for the sequence in the subdiagonal d>=1 (main diagonal: d=0) of triangle A064094 is N(d,x)/(1-x)^d.

Row sums give A001761(n+1). Main diagonal gives A000957(n+1), n >= 0.

Examples

			Triangle begins:
  1;
  1, 0;
  1, 2,  1;       N(3,x) = 1+2*x+x^2 = (1+x)^2.
  1, 10, 17,  2;
  1, 37, 181, 111, 6;
  ...
		

Crossrefs

Cf. A000957, A001761, A064094.

Formula

a(n, m) = [x^m]N(n, x); N(n, x) = (1-x)^(n-1) + Sum_{k=1..n-1} A064308(n-1, k)*k!*x^k*(1-x)^(n-1-k) for n >= 2; N(1, x) = 1 = N(2, x).