A174159 -id:A174159 - cp's OEIS frontend

A356118 Row sums of A174159.

1, 1, 2, 7, 34, 198, 1308, 9651, 79210, 720898, 7240804, 79774814, 957795188, 12453298700, 174353907960, 2615339041155, 41845544418330, 711374726547210, 12804746933817300, 243290199050400810, 4865804009789159580, 102181884318952612980, 2248001455463732796360

Offset: 0

Peter Luschny, Jul 27 2022

nonn

Cf. A174159.

a[n_] := Sum[A174159[n, k], {k, 0, n}]; Table[a[n], {n, 0, 22}]

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

Original entry on oeis.org

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, 224, 330, 99, 1, 1, 37, 77, 105, 291, 906, 513, 567, 817, 2883, 957, 811, 1466, 219, 1, 1, 50, 120, 188, 108, 548, 2020, 2632, 1508, 1682, 2356, 10116, 5574, 11724, 978, 4184, 18128, 8436, 2722, 5668, 466, 1

Offset: 0

Peter Luschny, Jul 28 2022

			Triangle T(n, k) begins:
[0] 1;
[1] 1;
[2] 1,   1;
[3] 1,   5,  1;
[4] 1, [10,  6],  16,   1;
[5] 1, [17, 25], [54,  58], 42,  1;
[6] 1, [26, 46,  27], [137, 354, 63], [224, 330],   99,   1;
[7] 1, [37, 77, 105], [291, 906, 513, 567], [817, 2883, 957],[811, 1466], 219, 1;

Peter Luschny, Permutations with Lehmer, a SageMath Jupyter Notebook.

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

for n in range(8):
    print([n], [A355776(n, k) + A355777(n, k)
        for k in range(number_of_partitions(n))])

cp's OEIS Frontend

A356118 Row sums of A174159.

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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.

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SageMath