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A347071 E.g.f.: exp(x) * (sec(x) - tan(x)) / (1 - x).

%I A347071 #10 Jun 11 2022 11:46:12
%S A347071 1,1,2,5,20,95,580,3999,32272,288783,2898300,31807679,382253808,
%T A347071 4964649079,69546528636,1042802172359,16688865840384,283667092507743,
%U A347071 5106507590277564,97017597229232975,1940428937186428720,40747978365579886375,896469940257304900700
%N A347071 E.g.f.: exp(x) * (sec(x) - tan(x)) / (1 - x).
%C A347071 Inverse boustrophedon transform of A000522.
%C A347071 Binomial transform of A337445.
%H A347071 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A347071 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A000522(k) * A000111(n-k).
%F A347071 a(n) = Sum_{k=0..n} binomial(n,k) * A337445(k).
%F A347071 a(n) ~ n! * exp(1)*(1 - sin(1))/cos(1). - _Vaclav Kotesovec_, Aug 23 2021
%t A347071 nmax = 22; CoefficientList[Series[Exp[x] (Sec[x] - Tan[x])/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
%t A347071 t[n_, 0] := n! Sum[1/k!, {k, 0, n}]; 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, 22}]
%o A347071 (Python)
%o A347071 from itertools import count, islice, accumulate
%o A347071 from operator import sub
%o A347071 def A347071_gen(): # generator of terms
%o A347071     blist, m = tuple(), 1
%o A347071     for i in count(1):
%o A347071         yield (blist := tuple(accumulate(reversed(blist),func=sub,initial=m)))[-1]
%o A347071         m = m*i + 1
%o A347071 A347071_list = list(islice(A347071_gen(),30)) # _Chai Wah Wu_, Jun 11 2022
%Y A347071 Cf. A000111, A000522, A307593, A337445.
%K A347071 nonn
%O A347071 0,3
%A A347071 _Ilya Gutkovskiy_, Aug 15 2021