A307879 Expansion of e.g.f. exp(4*x)*(sec(x) + tan(x)).

1, 5, 25, 126, 645, 3380, 18285, 103036, 610345, 3833540, 25714345, 185107596, 1433220045, 11932724900, 106613406405, 1019012112556, 10382757537745, 112378069315460, 1287787864054465, 15576862520435916, 198330820236011445, 2651486893149253220, 37135749401704458525

Offset: 0

Author

Ilya Gutkovskiy, Jun 04 2019

Keywords

• nonn

Comments

Boustrophedon transform of A000302 (powers of 4).

Links

• Index entries for sequences related to boustrophedon transform

Crossrefs

Column k=4 of A292975.

Cf. A000111, A000302, A000752, A307878.

Programs

Mathematica

nmax = 22; CoefficientList[Series[Exp[4 x] (Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := 4^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 A307879_gen(): # generator of terms
    blist, m = tuple(), 1
    yield from blist
    while True:
        yield (blist := tuple(accumulate(reversed(blist),initial=m)))[-1]
        m *= 4
A307879_list = list(islice(A307879_gen(),40)) # Chai Wah Wu, Jun 12 2022