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Search: id:A107053
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| A107053 |
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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). |
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11
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| 1, 4, 4, 76, 307, 380989, 13464073, 3084163593839, 6109976845914041, 694491088545589897439, 1664245369537759004769053, 82473629015170976645702130970352147
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sum_{k>=0} a(k)/A107054(k) = 14.052297927432224441845709796250699506418496460894575328...
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FORMULA
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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).
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EXAMPLE
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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, ...}
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PROGRAM
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(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]))}
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CROSSREFS
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Cf. A107052, A107045/A107046, A107047/A107048 (y=2), A107049/A107050 (y=3), A107051/A107052 (y=4).
Adjacent sequences: A107050 A107051 A107052 this_sequence A107054 A107055 A107056
Sequence in context: A009644 A124399 A119600 this_sequence A068376 A131592 A092209
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KEYWORD
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nonn,frac
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 10 2005
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