|
Search: id:A107046
|
|
|
| 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). |
|
+0
12
|
|
| 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
(list; table; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
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; ...
|
|
PROGRAM
|
(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: A134434 A139809 A094099 this_sequence A072907 A059833 A123152
Adjacent sequences: A107043 A107044 A107045 this_sequence A107047 A107048 A107049
|
|
KEYWORD
|
nonn,tabl,frac
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), May 10 2005
|
|
|
Search completed in 0.002 seconds
|
