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URL: https://oeis.org/A307710

⇱ A307710 - OEIS

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A307710
a(n) is the determinant of the Vandermonde matrix of the digits of n in factorial base.
1
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.
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.
Sequence in context: A127842 A127512 A263787 * A112207 A112208 A339089
KEYWORD
sign,base
AUTHOR
Rémy Sigrist, Apr 23 2019
STATUS
approved