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

0,6

Links

Table of n, a(n) for n=0..66.

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

Example

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;

Prog

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

Crossrefs

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

Sequence in context: A210651 A255831 A363970 * A188461 A188474 A173046

Adjacent sequences: A356110 A356111 A356112 * A356114 A356115 A356116

Keyword

nonn,tabf

Author

Peter Luschny, Jul 28 2022

Status

approved