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A308681 E.g.f.: (sec(x) - tan(x)) / sqrt(1 - 2*x).

%I A308681 #45 Jun 11 2022 11:45:28
%S A308681 1,0,2,7,60,519,5890,76637,1158808,19770383,377036646,7939301349,
%T A308681 183033429524,4584731740471,123994410402122,3601004174824573,
%U A308681 111771076844177328,3692510526181175583,129364120799128910158,4790645026641043053269,186981399898552187792620
%N A308681 E.g.f.: (sec(x) - tan(x)) / sqrt(1 - 2*x).
%C A308681 Inverse boustrophedon transform of A001147.
%H A308681 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A308681 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A001147(k) * A000111(n-k).
%F A308681 a(n) ~ (1 - sin(1/2)) * 2^(n + 1/2) * n^n / (cos(1/2) * exp(n)). - _Vaclav Kotesovec_, Aug 23 2021
%t A308681 nmax = 20; CoefficientList[Series[(Sec[x] - Tan[x])/Sqrt[1 - 2 x], {x, 0, nmax}], x] Range[0, nmax]!
%t A308681 t[n_, 0] := (2 n - 1)!!; t[n_, k_] := t[n, k] = t[n, k - 1] - t[n - 1, n - k]; a[n_] := t[n, n]; Table[a[n], {n, 0, 20}]
%o A308681 (Python)
%o A308681 from itertools import count, islice, accumulate
%o A308681 from operator import sub
%o A308681 def A308681_gen(): # generator of terms
%o A308681     blist, m = tuple(), 1
%o A308681     for i in count(1):
%o A308681         yield (blist := tuple(accumulate(reversed(blist),func=sub,initial=m)))[-1]
%o A308681         m *= (2*i-1)
%o A308681 A308681_list = list(islice(A308681_gen(),30)) # _Chai Wah Wu_, Jun 11 2022
%Y A308681 Cf. A000111, A001147, A296792, A337445.
%K A308681 nonn
%O A308681 0,3
%A A308681 _Ilya Gutkovskiy_, Aug 15 2021