OFFSET
1,8
LINKS
Seiichi Manyama, Antidiagonals n = 1..140, flattened
FORMULA
G.f. of column k: Sum_{j>=1} mu(j)*j^k*x^j/(1 - x^j).
Dirichlet g.f. of column k: zeta(s)/zeta(s-k).
A(n,k) = Sum_{d|n} mu(d)*d^k.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, -1, -3, -7, -15, -31, ...
0, -2, -8, -26, -80, -242, ...
0, -1, -3, -7, -15, -31, ...
0, -4, -24, -124, -624, -3124, ...
0, 2, 24, 182, 1200, 7502, ...
MATHEMATICA
Table[Function[k, Product[1 - Boole[PrimeQ[d]] d^k, {d, Divisors[n]}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten
Table[Function[k, SeriesCoefficient[Sum[MoebiusMu[j] j^k x^j/(1 - x^j), {j, 1, n}], {x, 0, n}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten
Table[Function[k, Sum[MoebiusMu[d] d^k, {d, Divisors[n]}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten
PROG
(PARI) T(n, k) = sumdiv(n, d, moebius(d)*d^k);
matrix(6, 6, n, k, T(n, k-1)) \\ Michel Marcus, Dec 03 2018
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Ilya Gutkovskiy, Dec 03 2018
STATUS
approved