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A347072 E.g.f.: -log(1 - x) * (sec(x) + tan(x)).

%I A347072 #9 Jun 12 2022 09:39:19
%S A347072 0,1,3,8,28,119,605,3597,24624,191481,1672273,16240509,173870156,
%T A347072 2036293453,25910852669,356057435177,5255621683776,82932788545297,
%U A347072 1393129225943169,24819194946609589,467369450831456492,9274872837974110805,193447045984755732413
%N A347072 E.g.f.: -log(1 - x) * (sec(x) + tan(x)).
%C A347072 Boustrophedon transform of shifted factorial numbers.
%H A347072 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A347072 a(n) = Sum_{k=0..n} binomial(n,k) * A104150(k) * A000111(n-k).
%F A347072 a(n) ~ (n-1)! * (1 + sin(1)) / cos(1). - _Vaclav Kotesovec_, Aug 23 2021
%t A347072 nmax = 22; CoefficientList[Series[-Log[1 - x] (Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A347072 t[n_, 0] := If[n == 0, 0, (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, 22}]
%o A347072 (Python)
%o A347072 from itertools import accumulate, count, islice
%o A347072 def A347072_gen(): # generator of terms
%o A347072     blist, m = (0,), 1
%o A347072     yield from blist
%o A347072     for i in count(1):
%o A347072         yield (blist := tuple(accumulate(reversed(blist),initial=m)))[-1]
%o A347072         m *= i
%o A347072 A347072_list = list(islice(A347072_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A347072 Cf. A000111, A009429, A104150, A230960, A230961.
%K A347072 nonn
%O A347072 0,3
%A A347072 _Ilya Gutkovskiy_, Aug 15 2021