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

0,4

Comments

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

Links

Table of n, a(n) for n=0..44.

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).

Example

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.

Sequence in context: A262985 A296786 A145141 * A267409 A104469 A144112

Adjacent sequences: A103357 A103358 A103359 * A103361 A103362 A103363

Keyword

easy,frac,nonn,tabl

Author

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

Status

approved