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A363154
Triangle read by rows. The Hadamard product of A173018 and A349203.
3
1, 1, 0, 2, 1, 0, 3, 4, 1, 0, 12, 33, 22, 3, 0, 10, 52, 66, 26, 2, 0, 60, 570, 1208, 906, 228, 10, 0, 105, 1800, 5955, 7248, 3573, 600, 15, 0, 280, 8645, 42930, 78095, 62476, 21465, 2470, 35, 0, 252, 14056, 102256, 264702, 312380, 176468, 43824, 3514, 28, 0
OFFSET
0,4
FORMULA
T(n, k) = A173018(n, k) * A349203(n, k).
Sum_{k=0..n} (-1)^k * T(n, k) = lcm(1, 2, ..., n+1)*Bernoulli(n, 1) = A362994(n).
EXAMPLE
Triangle T(n, k) starts:
[0] 1;
[1] 1, 0;
[2] 2, 1, 0;
[3] 3, 4, 1, 0;
[4] 12, 33, 22, 3, 0;
[5] 10, 52, 66, 26, 2, 0;
[6] 60, 570, 1208, 906, 228, 10, 0;
[7] 105, 1800, 5955, 7248, 3573, 600, 15, 0;
[8] 280, 8645, 42930, 78095, 62476, 21465, 2470, 35, 0;
MAPLE
A173018 := (n, k) -> combinat[eulerian1](n, k):
A349203 := (n, k) -> ilcm(seq(binomial(n, j), j = 0..n)) / binomial(n, k):
A363154 := (n, k) -> A173018(n, k) * A349203(n, k):
for n from 0 to 8 do seq(A363154(n, k), k = 0..n) od;
CROSSREFS
Cf. A173018, A349203, A002944 (column 0), A099946, A362994 (alternating row sums), A362990 (row sums).
Sequence in context: A257566 A345117 A188286 * A101603 A228161 A124030
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, May 21 2023
STATUS
approved