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Search: id:A107051
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| A107051 |
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Numerators of coefficients that satisfy: 4^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = a(k)/A107052(k). |
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11
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| 1, 3, 9, 5, 127, 124273, 385829, 70009765747, 220026935042111, 59574747365570286907, 113453152114585319883313, 4471148647570383262775217527741887
(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)/A107052(k) = 8.2025187671791748426202820386803825244610468145759213023...
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FORMULA
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a(n)/A107052(n) = Sum_{k=0..n} T(n, k)*4^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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4^0 = 1;
4^1 = 1 + (3)*1;
4^2 = 1 + (3)*2 + (9/4)*2^2;
4^3 = 1 + (3)*3 + (9/4)*3^2 + (5/4)*3^3;
4^4 = 1 + (3)*4 + (9/4)*4^2 + (5/4)*4^3 + (127/256)*4^4.
Initial coefficients are:
A107051/A107052 = {1, 3, 9/4, 5/4, 127/256, 124273/800000,
385829/9600000, 70009765747/7906012800000,
220026935042111/129532113715200000, ...}.
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PROGRAM
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(PARI) {a(n)=numerator(sum(k=0, n, 4^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), A107053/A107054 (y=5).
Sequence in context: A103934 A077384 A122943 this_sequence A020834 A153019 A021720
Adjacent sequences: A107048 A107049 A107050 this_sequence A107052 A107053 A107054
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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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