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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.
0
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
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
KEYWORD
nonn,tabf
AUTHOR
Peter Luschny, Jul 28 2022
STATUS
approved