A107045 Numerators of the triangle of coefficients T(n,k), read by rows, that satisfy: y^x = Sum_{n=0..x} R_n(y)*x^n for all nonnegative integers x, y, where R_n(y) = Sum_{k=0..n} T(n,k)*y^k and T(n,k) = a(n,k)/A107046(n,k).

1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -11, 1, 1, -1, 1, -677, -61, 7, 1, -1, 1, 15311, -259, -1, 7, 1, -1, 1, 1170049273, -971891, -54407, 407, 23, 1, -1, 1, 541293087149, 426148171, -15993079, -58573, 829, 17, 1, -1, 1, -15074636799365429, 31108643619709, -23328513449, -138374321, -53429, 1501, 47, 1

Offset

0,11

Links

Table of n, a(n) for n=0..52.

Formula

Numerators of the matrix inverse of triangle A079901(n, k) = n^k.

Example

These are the numerators of the triangle that begins:
1;
-1,1;
1/4,-1/2,1/4;
-1/108,1/18,-1/12,1/27;
-11/6912,1/576,1/192,-1/108,1/256;
-677/21600000,-61/360000,7/24000,1/2700,-1/1280,1/3125; ...
which equals the matrix inverse of triangle A079901(n,k)=n^k:
1;
1,1;
1,2,4;
1,3,9,27;
1,4,16,64,256;
1,5,25,125,625,3125; ...

Prog

(PARI) a(n, k)=numerator((matrix(n+1, n+1, r, c, if(r>=c, (r-1)^(c-1)))^-1)[n+1, k+1])

Crossrefs

Cf. A079901, A107046, A107047/A107048 (y=2), A107049/A107050 (y=3), A107051/A107052 (y=4), A107053/A107054 (y=5).

Sequence in context: A130837 A010194 A280443 * A351449 A145140 A010195

Adjacent sequences: A107042 A107043 A107044 * A107046 A107047 A107048

Keyword

sign,tabl,frac

Author

Paul D. Hanna, May 10 2005

Status

approved