A307878 Expansion of e.g.f. exp(3*x)*(sec(x) + tan(x)).

1, 4, 16, 65, 272, 1189, 5506, 27365, 147512, 868129, 5589646, 39309965, 300724652, 2489776969, 22192420786, 211923843365, 2158631018192, 23361793658209, 267706067651926, 3238110860029565, 41228900865842132, 551189774407729849, 7719762678323791066

Offset: 0

Author

Ilya Gutkovskiy, Jun 04 2019

Keywords

• nonn

Comments

Boustrophedon transform of A000244 (powers of 3).

Links

• Index entries for sequences related to boustrophedon transform

Crossrefs

Column k=3 of A292975.

Cf. A000111, A000244, A000752, A307879.

Programs

Mathematica

nmax = 22; CoefficientList[Series[Exp[3 x] (Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := 3^n; 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, islice
def A307878_gen(): # generator of terms
    blist, m = tuple(), 1
    yield from blist
    while True:
        yield (blist := tuple(accumulate(reversed(blist),initial=m)))[-1]
        m *= 3
A307878_list = list(islice(A307878_gen(),40)) # Chai Wah Wu, Jun 12 2022