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

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

Author

Peter Luschny, Jul 28 2022

Keywords

• nonn
• tabf

Examples

			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;
		

Links

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

Crossrefs

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

Programs

SageMath

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