A307594 Expansion of e.g.f. (sec(x) + tan(x))*exp(-x)/(1 - x).

1, 1, 2, 7, 28, 145, 880, 6221, 50048, 452097, 4531440, 49919461, 599595192, 7799387921, 109232872424, 1638888843541, 26226252579296, 445889920626817, 8026518496420896, 152509898418037765, 3050274960962524520, 64056803495548131665, 1409264093116606297080

Offset: 0

Author

Ilya Gutkovskiy, Apr 17 2019

Keywords

• nonn

Comments

Boustrophedon transform of A000166.

Links

• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A000111, A000166, A230960, A307593.

Programs

Mathematica

nmax = 22; CoefficientList[Series[(Sec[x] + Tan[x]) Exp[-x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := (-1)^n HypergeometricPFQ[{-n, 1}, {}, 1]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 23, 0]

Python

from itertools import accumulate, count, islice
def A307594_gen(): # generator of terms
    blist, a, b = tuple(), 1, -1
    for n in count(1):
        yield (blist := tuple(accumulate(reversed(blist),initial=a)))[-1]
        a, b = a*n+b, -b
A307594_list = list(islice(A307594_gen(),30)) # Chai Wah Wu, Jun 11 2022