%I A103361
%S A103361 1,0,1,1,1,1,1,1,1,1,3,23,29,25,1,11,79,131,353,403,1,53,1237,4031,3451,
%T A103361 3101,749,1,103,5297,14213,34903,126121,101297,31837,1,2199,100123,
%U A103361 106657,119129,1438599,6199951,6112397,455481,1
%V A103361 1,0,1,1,-1,1,1,-1,1,1,3,-23,29,-25,1,11,-79,131,-353,403,1,53,-1237,4031,
               -3451,3101,
%W A103361 -749,1,103,-5297,14213,-34903,126121,-101297,31837,1,2199,-100123,106657,
               -119129,
%X A103361 1438599,-6199951,6112397,-455481,1
%N A103361 Numerator of coefficient in the interpolation polynomial for initial 
               values of the factorial, read by rows.
%C A103361 Denominator N(n,n) of leading coefficient of the n-th polynomial = n-th 
               term of A053557. N(n,n)/D(n,n) = Sum{k=0..n}(-1)^k/k! = A000166/n! 
               = A053557/A053556, where D(n,n) is A103360.
%F A103361 N(n, k) in Sum{k=0..n}N(n, k)/D(n, k)*m^k=m!, m=0..n, with reduced fraction 
               N(n, k)/D(n, k) and D(n, k) is A103360. N(n, k)=a(n*(n+3)/2-k).
%e A103361 1; 1; 1/2*x^2-1/2*x+1; 1/3*x^3-1/2*x^2+1/6*x+1;
%e A103361 3/8*x^4-23/12*x^3+29/8*x^2-25/12*x+1;
%e A103361 11/30*x^5-79/24*x^4+131/12*x^3-353/24*x^2+403/60*x+1
%Y A103361 Cf. A103360, A000166, A053556, A053557.
%Y A103361 Sequence in context: A153834 A153707 A153708 this_sequence A136090 A032688 
               A142345
%Y A103361 Adjacent sequences: A103358 A103359 A103360 this_sequence A103362 A103363 
               A103364
%K A103361 easy,frac,sign,tabl
%O A103361 0,11
%A A103361 Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Feb 02 2005