

A107049


Numerators of coefficients that satisfy: 3^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = a(k)/A107050(k).


11



1, 2, 1, 11, 101, 71723, 1462111, 194269981673, 224103520039487, 14876670160046176873, 20871062802926443547323, 606768727432357137728440774281877, 97827345788163051844748893917483101
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OFFSET

0,2


COMMENTS

Sum_{k>=0} a(k)/A107050(k) = 4.5568226185870666883519278484116281050682807568451524897...


LINKS

Table of n, a(n) for n=0..12.


FORMULA

a(n)/A107050(n) = Sum_{k=0..n} T(n, k)*3^k where T(n, k) = A107045(n, k)/A107046(n, k) = [A079901^1](n, k) (matrix inverse of A079901).


EXAMPLE

3^0 = 1;
3^1 = 1 + (2)*1;
3^2 = 1 + (2)*2 + (1)*2^2;
3^3 = 1 + (2)*3 + (1)*3^2 + (11/27)*3^3;
3^4 = 1 + (2)*4 + (1)*4^2 + (11/27)*4^3 + (101/864)*4^4.
Initial coefficients are:
A107049/A107050 = {1, 2, 1, 11/27, 101/864, 71723/2700000,
1462111/291600000, 194269981673/240145138800000,
224103520039487/1967268977049600000, ...}.


PROG

(PARI) {a(n)=numerator(sum(k=0, n, 3^k*(matrix(n+1, n+1, r, c, if(r>=c, (r1)^(c1)))^1)[n+1, k+1]))}


CROSSREFS

Cf. A107045/A107046, A107047/A107048 (y=2), A107051/A107052 (y=4), A107053/A107054 (y=5).
Sequence in context: A012900 A009288 A082272 * A074956 A176088 A069566
Adjacent sequences: A107046 A107047 A107048 * A107050 A107051 A107052


KEYWORD

nonn,frac


AUTHOR

Paul D. Hanna, May 10 2005


STATUS

approved



