cp's OEIS Frontend

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

%I A363154 #10 May 02 2024 09:45:36
%S A363154 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,
%T A363154 10,0,105,1800,5955,7248,3573,600,15,0,280,8645,42930,78095,62476,
%U A363154 21465,2470,35,0,252,14056,102256,264702,312380,176468,43824,3514,28,0
%N A363154 Triangle read by rows. The Hadamard product of A173018 and A349203.
%H A363154 Peter Luschny, <a href="https://mathoverflow.net/q/447278">A combinatorial triangle for the Bernoulli numbers</a>, MathOverflow 2023.
%F A363154 T(n, k) = A173018(n, k) * A349203(n, k).
%F A363154 Sum_{k=0..n} (-1)^k * T(n, k) = lcm(1, 2, ..., n+1)*Bernoulli(n, 1) = A362994(n).
%e A363154 Triangle T(n, k) starts:
%e A363154 [0]   1;
%e A363154 [1]   1,    0;
%e A363154 [2]   2,    1,     0;
%e A363154 [3]   3,    4,     1,     0;
%e A363154 [4]  12,   33,    22,     3,     0;
%e A363154 [5]  10,   52,    66,    26,     2,     0;
%e A363154 [6]  60,  570,  1208,   906,   228,    10,    0;
%e A363154 [7] 105, 1800,  5955,  7248,  3573,   600,   15,  0;
%e A363154 [8] 280, 8645, 42930, 78095, 62476, 21465, 2470, 35, 0;
%p A363154 A173018 := (n, k) -> combinat[eulerian1](n, k):
%p A363154 A349203 := (n, k) -> ilcm(seq(binomial(n, j), j = 0..n)) / binomial(n, k):
%p A363154 A363154 := (n, k) -> A173018(n, k) * A349203(n, k):
%p A363154 for n from 0 to 8 do seq(A363154(n, k), k = 0..n) od;
%Y A363154 Cf. A173018, A349203, A002944 (column 0), A099946, A362994 (alternating row sums), A362990 (row sums).
%K A363154 nonn,tabl
%O A363154 0,4
%A A363154 _Peter Luschny_, May 21 2023