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A307592
Expansion of e.g.f. (sec(x) + tan(x))*(1 - LambertW(-x)*(2 + LambertW(-x))/2).
0
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.
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 17 2019
STATUS
approved