A307592 Expansion of e.g.f. (sec(x) + tan(x))*(1 - LambertW(-x)*(2 + LambertW(-x))/2).

1, 2, 4, 11, 47, 296, 2638, 31184, 460445, 8121616, 166019736, 3851820576, 99905492939, 2863509479104, 89861971946594, 3064181181957632, 112806282518694969, 4459192457431503104, 188376562263115020076, 8469292812455408254464, 403767081039021522624615

Offset

0,2

Comments

Boustrophedon transform of A000272.

Links

Table of n, a(n) for n=0..20.

Index entries for sequences related to boustrophedon transform

Formula

a(n) ~ (1 + sin(exp(-1)))/cos(exp(-1)) * n^(n-2). - Vaclav Kotesovec, Aug 17 2019

Mathematica

nmax = 20; CoefficientList[Series[(Sec[x] + Tan[x]) (1 - LambertW[-x] (2 + LambertW[-x])/2), {x, 0, nmax}], x] Range[0, nmax]!
t[n_, 0] := If[n < 1, 1, n^(n - 2)]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 21, 0]

Prog

(Python)
from itertools import islice, count, accumulate
def A307592_gen(): # generator of terms
    blist = (1, 2)
    yield from blist
    for i in count(2):
        yield (blist := tuple(accumulate(reversed(blist), initial=i**(i-2))))[-1]
A307592_list = list(islice(A307592_gen(), 30)) # Chai Wah Wu, Jun 11 2022

Crossrefs

Cf. A000111, A000272, A306880, A306881.

Sequence in context: A134019 A120259 A174632 * A091240 A068488 A096119

Adjacent sequences: A307589 A307590 A307591 * A307593 A307594 A307595

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 17 2019

Status

approved