A107050 Denominators of coefficients that satisfy: 3^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = A107049(k)/a(k).

1, 1, 1, 27, 864, 2700000, 291600000, 240145138800000, 1967268977049600000, 1045487392432216473600000, 13068592405402705920000000000, 3728621931719673008255139717120000000000

Offset

0,4

Links

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

Formula

A107049(n)/a(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)=denominator(sum(k=0, n, 3^k*(matrix(n+1, n+1, r, c, if(r>=c, (r-1)^(c-1)))^-1)[n+1, k+1]))}

Crossrefs

Cf. A107049, A107045/A107046, A107047/A107048 (y=2), A107051/A107052 (y=4), A107053/A107054 (y=5).

Sequence in context: A120715 A065922 A061695 * A129999 A132059 A292362

Adjacent sequences: A107047 A107048 A107049 * A107051 A107052 A107053

Keyword

nonn,frac

Author

Paul D. Hanna, May 10 2005

Status

approved