A362990 -id:A362990 - cp's OEIS frontend

A363154 Triangle read by rows. The Hadamard product of A173018 and A349203.

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

Peter Luschny, May 21 2023

			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;

Peter Luschny, A combinatorial triangle for the Bernoulli numbers, MathOverflow 2023.

Cf. A173018, A349203, A002944 (column 0), A099946, A362994 (alternating row sums), A362990 (row sums).

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;

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).

cp's OEIS Frontend

A363154 Triangle read by rows. The Hadamard product of A173018 and A349203.

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