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A337445 E.g.f.: 1 / ((sec(x) + tan(x)) * (1 - x)).

%I A337445 #17 Jun 11 2022 11:45:53
%S A337445 1,0,1,1,9,29,235,1373,12369,103385,1084371,11574289,141594233,
%T A337445 1818356773,25656355803,382941579733,6146456787873,104279900050865,
%U A337445 1879443080591011,35680329646116377,713976964110565065,14988564748268742269,329817773336305467819
%N A337445 E.g.f.: 1 / ((sec(x) + tan(x)) * (1 - x)).
%C A337445 Inverse boustrophedon transform of factorials.
%H A337445 Alois P. Heinz, <a href="/A337445/b337445.txt">Table of n, a(n) for n = 0..450</a>
%H A337445 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A337445 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * k! * A000111(n-k).
%F A337445 a(n) ~ n! * cos(1) / (1 + sin(1)). - _Vaclav Kotesovec_, Aug 31 2020
%p A337445 b:= proc(u, o) option remember;
%p A337445      `if`(u+o=0, 1, add(b(o-1+j, u-j), j=1..u))
%p A337445     end:
%p A337445 a:= proc(n) option remember; add((-1)^(n-k)
%p A337445       *binomial(n, k)*k!*b(n-k, 0), k=0..n)
%p A337445     end:
%p A337445 seq(a(n), n=0..23);  # _Alois P. Heinz_, Aug 15 2021
%t A337445 nmax = 22; CoefficientList[Series[1/((Sec[x] + Tan[x]) (1 - x)), {x, 0, nmax}], x] Range[0, nmax]!
%t A337445 t[n_, 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 A337445 (Python)
%o A337445 from itertools import count, islice, accumulate
%o A337445 from operator import sub
%o A337445 def A337445_gen(): # generator of terms
%o A337445     blist, m = tuple(), 1
%o A337445     for i in count(1):
%o A337445         yield (blist := tuple(accumulate(reversed(blist),func=sub,initial=m)))[-1]
%o A337445         m *= i
%o A337445 A337445_list = list(islice(A337445_gen(),30)) # _Chai Wah Wu_, Jun 11 2022
%Y A337445 Cf. A000111, A000142, A230960, A230961.
%K A337445 nonn
%O A337445 0,5
%A A337445 _Ilya Gutkovskiy_, Aug 27 2020