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

1, 4, 4, 76, 307, 380989, 13464073, 3084163593839, 6109976845914041, 694491088545589897439, 1664245369537759004769053, 82473629015170976645702130970352147

Offset: 0

Author

Paul D. Hanna, May 10 2005

Keywords

• nonn
• frac

Comments

Sum_{k>=0} a(k)/A107054(k) = 14.052297927432224441845709796250699506418496460894575328...

Examples

			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, ...}
		

Crossrefs

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

Programs

PARI

{a(n)=numerator(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]))}

Formula

a(n)/A107054(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).