A307710 a(n) is the determinant of the Vandermonde matrix of the digits of n in factorial base.
1, 1, -1, 0, -2, -1, 0, 0, 0, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 6, -6, 0, -6, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0
Offset: 0
Examples
| 3^0 3^1 2^2 |
a(22) = a(3*3! + 2*2! + 0*1!) = det | 2^0 2^1 2^2 | = -6.
| 0^0 0^1 0^2 |
Links
Programs
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PARI
a(n) = my (d=[]); for (r=2, oo, if (n, d=concat(n%r,d); n\=r, return (matdet(matrix(#d, #d, r, c, d[r]^(c-1))))))
Formula
a(n) != 0 iff n belongs to A321682.
Comments