OFFSET
0,3
COMMENTS
Conjecture: For p prime, a(p) == -1 (mod p).
FORMULA
a(n) = Sum_{k=0..n} (-1)^(k+1)*k!*A062139(n, k + 1).
a(0) = 0, a(n) = n!*Sum_{k=1..n} (n-k+2)*(n-k+1)*(2^k-1)/(2*k).
a(n) = A000292(n)*n!*hypergeom([1 - n, 1, 1], [2, 4], -1). - Peter Luschny, Jun 30 2022
MAPLE
MATHEMATICA
CoefficientList[Series[Log[(1 - x)/(1 - 2*x)]/ (1 - x)^3, {x, 0, 20}], x]Table[n!, {n, 0, 20}] (* Stefano Spezia, Jun 30 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Mélika Tebni, Jun 30 2022
STATUS
approved