A307592 - OEIS

%I #10 Jun 11 2022 20:17:41

%S 1,2,4,11,47,296,2638,31184,460445,8121616,166019736,3851820576,

%T 99905492939,2863509479104,89861971946594,3064181181957632,

%U 112806282518694969,4459192457431503104,188376562263115020076,8469292812455408254464,403767081039021522624615

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

%C Boustrophedon transform of A000272.

%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>

%F a(n) ~ (1 + sin(exp(-1)))/cos(exp(-1)) * n^(n-2). - _Vaclav Kotesovec_, Aug 17 2019

%t nmax = 20; CoefficientList[Series[(Sec[x] + Tan[x]) (1 - LambertW[-x] (2 + LambertW[-x])/2), {x, 0, nmax}], x] Range[0, nmax]!

%t 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]

%o (Python)

%o from itertools import islice, count, accumulate

%o def A307592_gen(): # generator of terms

%o     blist = (1,2)

%o     yield from blist

%o     for i in count(2):

%o         yield (blist := tuple(accumulate(reversed(blist),initial=i**(i-2))))[-1]

%o A307592_list = list(islice(A307592_gen(),30)) # _Chai Wah Wu_, Jun 11 2022

%Y Cf. A000111, A000272, A306880, A306881.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 17 2019