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A337443 E.g.f.: (1 + x) * exp(x) / (sec(x) + tan(x)).

%I A337443 #8 Jun 11 2022 11:45:46
%S A337443 1,1,0,-1,-4,-5,-20,9,-208,855,-6180,41549,-321792,2651155,-23664420,
%T A337443 225865769,-2301032256,24901626095,-285356879940,3451591584869,
%U A337443 -43947119045600,587529302036875,-8228722825167940,120487046847246049,-1840906518665985824
%N A337443 E.g.f.: (1 + x) * exp(x) / (sec(x) + tan(x)).
%C A337443 Inverse boustrophedon transform of positive natural numbers.
%H A337443 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A337443 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * (k+1) * A000111(n-k).
%t A337443 nmax = 24; CoefficientList[Series[(1 + x) Exp[x]/(Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A337443 t[n_, 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, 24}]
%o A337443 (Python)
%o A337443 from itertools import count, islice, accumulate
%o A337443 from operator import sub
%o A337443 def A337443_gen(): # generator of terms
%o A337443     blist = tuple()
%o A337443     for i in count(1):
%o A337443         yield (blist := tuple(accumulate(reversed(blist),func=sub,initial=i)))[-1]
%o A337443 A337443_list = list(islice(A337443_gen(),30)) # _Chai Wah Wu_, Jun 11 2022
%Y A337443 Cf. A000027, A000111, A000737, A034428, A231179.
%K A337443 sign
%O A337443 0,5
%A A337443 _Ilya Gutkovskiy_, Aug 27 2020