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A322512
Triangle read by rows of the 2-adic valuation (A007814) of Stirling numbers of first kind (A008275).
0
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, 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, 3, 2, 1, 0, 1, 0, 1, 0, 1, 0, 10, 7, 7, 3, 2, 1, 0, 1, 0, 1, 0, 1, 0
OFFSET
1,11
LINKS
Min Qiu, Shaofang Hong, The 2-adic valuations of Stirling numbers of the first kind, arXiv:1812.04539 [math.NT], 2018.
FORMULA
T(n,k) = A007814(A008275(n,k)).
EXAMPLE
Triangle begins:
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, 2, 0,
...
MATHEMATICA
T[n_, k_] := IntegerExponent[StirlingS1[n, k], 2]; Table[T[n, k], {n, 1, 20}, {k, 1, n}] // Flatten (* Amiram Eldar, Dec 13 2018 *)
PROG
(PARI) T(n, k) = valuation(stirling(n, k, 1), 2);
row(n) = vector(n, k, T(n, k));
tabl(nn) = vector(nn, k, row(k)); (PARI) T(n, k) = valuation(stirling(n, k, 1), 2);
CROSSREFS
Sequence in context: A060096 A245756 A360672 * A152892 A193002 A366725
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Dec 13 2018
STATUS
approved