|
| |
|
|
A107047
|
|
Numerators of coefficients that satisfy: 2^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = a(k)/A107048(k).
|
|
11
|
|
|
|
1, 1, 1, 7, 77, 32387, 395159, 31824093937, 44855117331581, 1825389561156191099, 1571879809058619206897, 28070265610073576492663157851903, 2782861136717279135850604073374039
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
COMMENTS
|
Sum_{k>=0} a(k)/A107048(k) = 2.3276417590495914492697647475269004042620542650376396714...
|
|
|
LINKS
|
Table of n, a(n) for n=0..12.
|
|
|
FORMULA
|
a(n)/A107048(n) = Sum_{k=0..n} T(n, k)*2^k where T(n, k) = A107045(n, k)/A107046(n, k) = [A079901^-1](n, k) (matrix inverse of A079901).
|
|
|
EXAMPLE
|
2^0 = 1;
2^1 = 1 + 1;
2^2 = 1 + 1*2 + (1/4)*2^2;
2^3 = 1 + 1*3 + (1/4)*3^2 + (7/108)*3^3;
2^4 = 1 + 1*4 + (1/4)*4^2 + (7/108)*4^3 + (77/6912)*4^4.
Initial fractional coefficients are:
A107047/A107048 = {1, 1, 1/4, 7/108, 77/6912, 32387/21600000,
395159/2332800000, 31824093937/1921161110400000,
44855117331581/31476303632793600000, ... }.
|
|
|
PROG
|
(PARI) {a(n)=numerator(sum(k=0, n, 2^k*(matrix(n+1, n+1, r, c, if(r>=c, (r-1)^(c-1)))^-1)[n+1, k+1]))}
|
|
|
CROSSREFS
|
Cf. A107045/A107046, A107049/A107050 (y=3), A107051/A107052 (y=4), A107053/A107054 (y=5).
Sequence in context: A342347 A082782 A356437 * A210413 A045485 A068621
Adjacent sequences: A107044 A107045 A107046 * A107048 A107049 A107050
|
|
|
KEYWORD
|
nonn,frac
|
|
|
AUTHOR
|
Paul D. Hanna, May 10 2005
|
|
|
STATUS
|
approved
|
| |
|
|
