A307593 Expansion of e.g.f. (sec(x) + tan(x))*exp(x)/(1 - x).

1, 3, 10, 39, 180, 977, 6156, 44401, 361872, 3295025, 33193284, 366828033, 4414938000, 57501795977, 805984165252, 12098920460089, 193676009792768, 3293501718960033, 59294599560573508, 1126737323074730161, 22536528123718353104, 473290909667471110361

Offset: 0

Author

Ilya Gutkovskiy, Apr 17 2019

Keywords

• nonn

Comments

Boustrophedon transform of A000522.

Links

• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A000111, A000522, A230960, A307594.

Programs

Mathematica

nmax = 21; CoefficientList[Series[(Sec[x] + Tan[x]) Exp[x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := If[n < 1, 1, Floor[Exp[1] n!]]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 22, 0]

Python

from itertools import count, islice, accumulate
def A307593_gen(): # generator of terms
    blist, m = tuple(), 1
    for i in count(1):
        yield (blist := tuple(accumulate(reversed(blist),initial=m)))[-1]
        m = m*i + 1
A307593_list = list(islice(A307593_gen(),30)) # Chai Wah Wu, Jun 11 2022