A107046 Denominators of the triangle of coefficients T(n,k), read by rows, that satisfy: y^x = Sum_{n=0..x} R_n(y)*x^n for all nonnegative integers x, y, where R_n(y) = Sum_{k=0..n} T(n,k)*y^k and T(n,k) = A107045(n,k)/a(n,k).

1, 1, 1, 4, 2, 4, 108, 18, 12, 27, 6912, 576, 192, 108, 256, 21600000, 360000, 24000, 2700, 1280, 3125, 2332800000, 12960000, 2592000, 291600, 46080, 18750, 46656, 1921161110400000, 1524731040000, 43563744000, 700131600, 15805440, 918750

Offset

0,4

Links

Table of n, a(n) for n=0..33.

Formula

Denominators of the matrix inverse of triangle A079901(n, k) = n^k.

Example

These are the denominators of the triangle that begins:
1;
-1,1;
1/4,-1/2,1/4;
-1/108,1/18,-1/12,1/27;
-11/6912,1/576,1/192,-1/108,1/256;
-677/21600000,-61/360000,7/24000,1/2700,-1/1280,1/3125; ...
which equals the matrix inverse of triangle A079901(n,k)=n^k:
1;
1,1;
1,2,4;
1,3,9,27;
1,4,16,64,256;
1,5,25,125,625,3125; ...

Prog

(PARI) a(n, k)=denominator((matrix(n+1, n+1, r, c, if(r>=c, (r-1)^(c-1)))^-1)[n+1, k+1])

Crossrefs

Cf. A079901, A107045, A107047/A107048 (y=2), A107049/A107050 (y=3), A107051/A107052 (y=4), A107053/A107054 (y=5).

Sequence in context: A139809 A348640 A094099 * A267184 A275927 A072907

Adjacent sequences: A107043 A107044 A107045 * A107047 A107048 A107049

Keyword

nonn,tabl,frac

Author

Paul D. Hanna, May 10 2005

Status

approved