A373115 Number weak ascent sequences of length 2n (prefixed with a zero) with exactly n weak ascents.

1, 0, 0, 1, 35, 1661, 107002, 9047970, 972937247, 129603346139, 20934881571217, 4029204458109445, 910549073414709876, 238643240329544375336, 71772700696174395158056, 24544642886642172762170933, 9468192975202745545226891834, 4090995487728206638560153282674

Offset: 0

Author

Alois P. Heinz, May 25 2024

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..70
• Beata Benyi, Anders Claesson, and Mark Dukes, Weak ascent sequences and related combinatorial structures, arXiv:2111.03159 [math.CO], 2021-2022.

Crossrefs

Cf. A357141, A369321.

Programs

Maple

b:= proc(n, i, t) option remember; expand(`if`(n=0, 1, add(
      b(n-1, j, t+`if`(j>=i, 1, 0))*`if`(j>=i, x, 1), j=0..t+1)))
    end:
a:= n-> coeff(b(2*n, -1$2), x, n):
seq(a(n), n=0..17);

Formula

a(n) = A369321(2n,n).