A356113 - OEIS

%I #12 Aug 23 2022 05:21:37

%S 1,1,1,1,1,5,1,1,10,6,16,1,1,17,25,54,58,42,1,1,26,46,27,137,354,63,

%T 224,330,99,1,1,37,77,105,291,906,513,567,817,2883,957,811,1466,219,1,

%U 1,50,120,188,108,548,2020,2632,1508,1682,2356,10116,5574,11724,978,4184,18128,8436,2722,5668,466,1

%N Triangle read by rows. T(n, k) = A355776(n, k) + A355777(n, k). Refining A174159, the Euler minus Narayana/Catalan triangle.

%H Peter Luschny, <a href="https://github.com/PeterLuschny/PermutationsWithLehmer/blob/main/PermutationsWithLehmer.ipynb">Permutations with Lehmer</a>, a SageMath Jupyter Notebook.

%e Triangle T(n, k) begins:

%e [0] 1;

%e [1] 1;

%e [2] 1,   1;

%e [3] 1,   5,  1;

%e [4] 1, [10,  6],  16,   1;

%e [5] 1, [17, 25], [54,  58], 42,  1;

%e [6] 1, [26, 46,  27], [137, 354, 63], [224, 330],   99,   1;

%e [7] 1, [37, 77, 105], [291, 906, 513, 567], [817, 2883, 957],[811, 1466], 219, 1;

%o (SageMath)

%o for n in range(8):

%o     print([n], [A355776(n, k) + A355777(n, k)

%o         for k in range(number_of_partitions(n))])

%Y Cf. A355776, A355777, A356118 (row sums), A174159 (reduced triangle).

%K nonn,tabf

%O 0,6

%A _Peter Luschny_, Jul 28 2022