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A356113 Triangle read by rows. T(n, k) = A355776(n, k) + A355777(n, k). Refining A174159, the Euler minus Narayana/Catalan triangle.

%I A356113 #12 Aug 23 2022 05:21:37
%S A356113 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 A356113 224,330,99,1,1,37,77,105,291,906,513,567,817,2883,957,811,1466,219,1,
%U A356113 1,50,120,188,108,548,2020,2632,1508,1682,2356,10116,5574,11724,978,4184,18128,8436,2722,5668,466,1
%N A356113 Triangle read by rows. T(n, k) = A355776(n, k) + A355777(n, k). Refining A174159, the Euler minus Narayana/Catalan triangle.
%H A356113 Peter Luschny, <a href="https://github.com/PeterLuschny/PermutationsWithLehmer/blob/main/PermutationsWithLehmer.ipynb">Permutations with Lehmer</a>, a SageMath Jupyter Notebook.
%e A356113 Triangle T(n, k) begins:
%e A356113 [0] 1;
%e A356113 [1] 1;
%e A356113 [2] 1,   1;
%e A356113 [3] 1,   5,  1;
%e A356113 [4] 1, [10,  6],  16,   1;
%e A356113 [5] 1, [17, 25], [54,  58], 42,  1;
%e A356113 [6] 1, [26, 46,  27], [137, 354, 63], [224, 330],   99,   1;
%e A356113 [7] 1, [37, 77, 105], [291, 906, 513, 567], [817, 2883, 957],[811, 1466], 219, 1;
%o A356113 (SageMath)
%o A356113 for n in range(8):
%o A356113     print([n], [A355776(n, k) + A355777(n, k)
%o A356113         for k in range(number_of_partitions(n))])
%Y A356113 Cf. A355776, A355777, A356118 (row sums), A174159 (reduced triangle).
%K A356113 nonn,tabf
%O A356113 0,6
%A A356113 _Peter Luschny_, Jul 28 2022