A107054 Denominators of coefficients that satisfy: 5^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = A107053(k)/a(k).

1, 1, 1, 27, 216, 675000, 72900000, 60036284700000, 491817244262400000, 261371848108054118400000, 3267148101350676480000000000, 932155482929918252063784929280000000000

Offset

0,4

Links

Table of n, a(n) for n=0..11.

Formula

A107053(n)/a(n) = Sum_{k=0..n} T(n, k)*5^k where T(n, k) = A107045(n, k)/A107046(n, k) = [A079901^-1](n, k) (matrix inverse of A079901).

Example

5^0 = 1;
5^1 = 1 + (4)*1;
5^2 = 1 + (4)*2 + (4)*2^2;
5^3 = 1 + (4)*3 + (4)*3^2 + (76/27)*3^3;
5^4 = 1 + (4)*4 + (4)*4^2 + (76/27)*4^3 + (307/216)*4^4.
Initial coefficients are:
A107053/A107054 = {1, 4, 4, 76/27, 307/216, 380989/675000,
13464073/72900000, 3084163593839/60036284700000,
6109976845914041/491817244262400000, ...}

Prog

(PARI) {a(n)=denominator(sum(k=0, n, 5^k*(matrix(n+1, n+1, r, c, if(r>=c, (r-1)^(c-1)))^-1)[n+1, k+1]))}

Crossrefs

Cf. A107051, A107045/A107046, A107047/A107048 (y=2), A107049/A107050 (y=3), A107051/A107052 (y=4).

Sequence in context: A059827 A117688 A272342 * A160441 A222994 A125364

Adjacent sequences: A107051 A107052 A107053 * A107055 A107056 A107057

Keyword

nonn,frac

Author

Paul D. Hanna, May 10 2005

Status

approved