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A307594 Expansion of e.g.f. (sec(x) + tan(x))*exp(-x)/(1 - x).

%I A307594 #8 Jun 11 2022 20:22:06
%S A307594 1,1,2,7,28,145,880,6221,50048,452097,4531440,49919461,599595192,
%T A307594 7799387921,109232872424,1638888843541,26226252579296,445889920626817,
%U A307594 8026518496420896,152509898418037765,3050274960962524520,64056803495548131665,1409264093116606297080
%N A307594 Expansion of e.g.f. (sec(x) + tan(x))*exp(-x)/(1 - x).
%C A307594 Boustrophedon transform of A000166.
%H A307594 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%t A307594 nmax = 22; CoefficientList[Series[(Sec[x] + Tan[x]) Exp[-x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
%t A307594 t[n_, 0] := (-1)^n HypergeometricPFQ[{-n, 1}, {}, 1]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 23, 0]
%o A307594 (Python)
%o A307594 from itertools import accumulate, count, islice
%o A307594 def A307594_gen(): # generator of terms
%o A307594     blist, a, b = tuple(), 1, -1
%o A307594     for n in count(1):
%o A307594         yield (blist := tuple(accumulate(reversed(blist),initial=a)))[-1]
%o A307594         a, b = a*n+b, -b
%o A307594 A307594_list = list(islice(A307594_gen(),30)) # _Chai Wah Wu_, Jun 11 2022
%Y A307594 Cf. A000111, A000166, A230960, A307593.
%K A307594 nonn
%O A307594 0,3
%A A307594 _Ilya Gutkovskiy_, Apr 17 2019