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 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 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

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Last modified March 22 15:35 EDT 2023. Contains 361432 sequences. (Running on oeis4.)