A347072 E.g.f.: -log(1 - x) * (sec(x) + tan(x)).

0, 1, 3, 8, 28, 119, 605, 3597, 24624, 191481, 1672273, 16240509, 173870156, 2036293453, 25910852669, 356057435177, 5255621683776, 82932788545297, 1393129225943169, 24819194946609589, 467369450831456492, 9274872837974110805, 193447045984755732413

Offset: 0

Author

Ilya Gutkovskiy, Aug 15 2021

Keywords

• nonn

Comments

Boustrophedon transform of shifted factorial numbers.

Links

• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A000111, A009429, A104150, A230960, A230961.

Programs

Mathematica

nmax = 22; CoefficientList[Series[-Log[1 - x] (Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := If[n == 0, 0, (n - 1)!]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Table[a[n], {n, 0, 22}]

Python

from itertools import accumulate, count, islice
def A347072_gen(): # generator of terms
    blist, m = (0,), 1
    yield from blist
    for i in count(1):
        yield (blist := tuple(accumulate(reversed(blist),initial=m)))[-1]
        m *= i
A347072_list = list(islice(A347072_gen(),40)) # Chai Wah Wu, Jun 12 2022

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A104150(k) * A000111(n-k).

a(n) ~ (n-1)! * (1 + sin(1)) / cos(1). - Vaclav Kotesovec, Aug 23 2021