A103360 Denominator of coefficient in the interpolation polynomial for initial values of the factorial, read by row.

1, 1, 1, 2, 2, 1, 3, 2, 6, 1, 8, 12, 8, 12, 1, 30, 24, 12, 24, 60, 1, 144, 240, 144, 48, 36, 20, 1, 280, 720, 240, 144, 240, 180, 140, 1, 5760, 10080, 960, 180, 640, 1440, 1440, 280, 1

Offset: 0

Author

Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Feb 02 2005

Keywords

• easy
• frac
• nonn
• tabl

Comments

N(n,n)/D(n,n) = Sum{k=0..n}(-1)^k/k! = A000166/n! = A053557/A053556, where N(n,n) is A103361.

Examples

			1; 1; 1/2*x^2-1/2*x+1; 1/3*x^3-1/2*x^2+1/6*x+1;
3/8*x^4-23/12*x^3+29/8*x^2-25/12*x+1;
11/30*x^5-79/24*x^4+131/12*x^3-353/24*x^2+403/60*x+1
		

Crossrefs

Cf. A103361, A000166, A053556, A053557.

Formula

D(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 N(n, k) is A103361. D(n, k)=a(n*(n+3)/2-k).