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

0,5

Comments

This sequence is a variant of A307651, and has infinitely many nonzero terms.

Links

Table of n, a(n) for n=0..81.

Wikipedia, Vandermonde matrix

Index entries for sequences related to factorial base representation

Formula

a(n) != 0 iff n belongs to A321682.

Example

                                    | 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 |

Prog

(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))))))

Crossrefs

See A307651 for the decimal variant.

Cf. A108731, A321682.

Sequence in context: A127842 A127512 A263787 * A112207 A112208 A339089

Adjacent sequences: A307707 A307708 A307709 * A307711 A307712 A307713

Keyword

sign,base

Author

Rémy Sigrist, Apr 23 2019

Status

approved