%I #6 Jul 25 2022 08:02:58

%S 1,1,0,1,2,1,1,10,17,2,1,37,181,111,6,1,126,1530,2624,741,18,1,422,

%T 11607,43940,34063,4950,57,1,1422,83823,616894,1013799,412698,33337,

%U 186,1,4853,593203,7846573,23794925

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

%C 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.

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

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

%e Triangle begins:

%e 1;

%e 1, 0;

%e 1, 2, 1; N(3,x) = 1+2*x+x^2 = (1+x)^2.

%e 1, 10, 17, 2;

%e 1, 37, 181, 111, 6;

%e ...

%Y Cf. A000957, A001761, A064094.

%K nonn,tabl

%O 1,5

%A _Wolfdieter Lang_, Sep 13 2001