A103361 - OEIS

A103361

Numerator of coefficient in the interpolation polynomial for initial values of the factorial, read by rows.

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, -749, 1, 103, -5297, 14213, -34903, 126121, -101297, 31837, 1, 2199, -100123, 106657, -119129, 1438599, -6199951, 6112397, -455481, 1

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OFFSET

0,11

COMMENTS

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.

LINKS

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

FORMULA

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).

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. A103360, A000166, A053556, A053557.

Sequence in context: A232327 A153708 A109218 * A136090 A032688 A142345

Adjacent sequences: A103358 A103359 A103360 * A103362 A103363 A103364

KEYWORD

easy,frac,sign,tabl

AUTHOR

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

STATUS

approved