|
%I #8 Dec 13 2018 04:59:24
%S 0,0,0,1,0,0,1,0,1,0,3,1,0,1,0,3,1,0,0,0,0,4,2,3,0,0,0,0,4,2,2,0,3,1,
%T 2,0,7,4,2,2,0,3,1,2,0,7,4,2,5,0,0,1,1,0,0,8,5,3,2,1,0,0,1,3,0,0,8,5,
%U 3,2,1,0,1,0,1,0,1,0,10,7,7,3,2,1,0,1,0,1,0,1,0
%N Triangle read by rows of the 2-adic valuation (A007814) of Stirling numbers of first kind (A008275).
%H Min Qiu, Shaofang Hong, <a href="https://arxiv.org/abs/1812.04539">The 2-adic valuations of Stirling numbers of the first kind</a>, arXiv:1812.04539 [math.NT], 2018.
%F T(n,k) = A007814(A008275(n,k)).
%e Triangle begins:
%e 0,
%e 0, 0,
%e 1, 0, 0,
%e 1, 0, 1, 0,
%e 3, 1, 0, 1, 0,
%e 3, 1, 0, 0, 0, 0,
%e 4, 2, 3, 0, 0, 0, 0,
%e 4, 2, 2, 0, 3, 1, 2, 0,
%e ...
%t T[n_, k_] := IntegerExponent[StirlingS1[n, k], 2]; Table[T[n, k], {n, 1, 20}, {k, 1, n}] // Flatten (* _Amiram Eldar_, Dec 13 2018 *)
%o (PARI) T(n,k) = valuation(stirling(n, k, 1), 2);
%o row(n) = vector(n, k, T(n,k));
%o tabl(nn) = vector(nn, k, row(k));(PARI) T(n,k) = valuation(stirling(n, k, 1), 2);
%Y Cf. A007814, A008275.
%K nonn,tabl
%O 1,11
%A _Michel Marcus_, Dec 13 2018
|
