OFFSET
1,2
COMMENTS
Row sums = A129502: (1, 3, 0, 6, 0, 0, 0, 10, 0, 0, ...).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275
FORMULA
T(n,k) = A317673(n/k) for k | n, T(n,k) = 0 otherwise. - Andrew Howroyd, Aug 03 2018
EXAMPLE
First few rows of the triangle are:
1;
2, 1;
-1, 0, 1;
3, 2, 0, 1;
-1, 0, 0, 0, 1;
-2, -1, 2, 0, 0, 1;
-1, 0, 0, 0, 0, 0, 1;
4, 3, 0, 2, 0, 0, 0, 1;
0, 0, -1, 0, 0, 0, 0, 0, 1;
...
MATHEMATICA
b[n_] := Module[{e}, Sum[e = IntegerExponent[d, 2]; If[d == 2^e, MoebiusMu[n/d] Binomial[2 + e, 2], 0], {d, Divisors[n]}]];
T[n_, k_] := If[Divisible[n, k], b[n/k], 0];
Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 24 2019 *)
PROG
(PARI) T(n, k)={ if(n%k, 0, sumdiv(n/k, d, my(e=valuation(d, 2)); if(d==1<<e, moebius(n/(k*d))*binomial(2+e, 2), 0))) } \\ Andrew Howroyd, Aug 03 2018
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Gary W. Adamson, Apr 17 2007
EXTENSIONS
Terms a(56) and beyond from Andrew Howroyd, Aug 03 2018
STATUS
approved