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%I #11 Jun 12 2022 09:40:02
%S 1,0,1,0,4,-4,31,-144,379,-5560,8572,-263128,473485,-15744416,
%T 47003477,-1206879556,5944492012,-119190424496,876847239971,
%U -15100821637664,149690044061351,-2416631748015804,29675481449346820,-477579212590451988,6840036862556737337
%N E.g.f.: exp(exp(x) - 1) / (sec(x) + tan(x)).
%C Inverse boustrophedon transform of Bell numbers.
%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A000110(k) * A000111(n-k).
%t nmax = 24; CoefficientList[Series[Exp[Exp[x] - 1]/(Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
%t t[n_, 0] := BellB[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, 24}]
%o (Python)
%o from itertools import islice, accumulate
%o from operator import sub
%o def A337447_gen(): # generator of terms
%o yield from (1,0)
%o blist, alist = (1,0), (1,)
%o while True:
%o yield (blist := tuple(accumulate(reversed(blist),func=sub,initial=(alist := list(accumulate(alist, initial=alist[-1])))[-1])))[-1]
%o A337447_list = list(islice(A337447_gen(),30)) # _Chai Wah Wu_, Jun 11-12 2022
%Y Cf. A000110, A000111, A000764.
%K sign
%O 0,5
%A _Ilya Gutkovskiy_, Aug 27 2020
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