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A307878 Expansion of e.g.f. exp(3*x)*(sec(x) + tan(x)).

%I A307878 #30 Jun 12 2022 09:40:16
%S A307878 1,4,16,65,272,1189,5506,27365,147512,868129,5589646,39309965,
%T A307878 300724652,2489776969,22192420786,211923843365,2158631018192,
%U A307878 23361793658209,267706067651926,3238110860029565,41228900865842132,551189774407729849,7719762678323791066
%N A307878 Expansion of e.g.f. exp(3*x)*(sec(x) + tan(x)).
%C A307878 Boustrophedon transform of A000244 (powers of 3).
%H A307878 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%t A307878 nmax = 22; CoefficientList[Series[Exp[3 x] (Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A307878 t[n_, 0] := 3^n; 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 A307878 (Python)
%o A307878 from itertools import accumulate, islice
%o A307878 def A307878_gen(): # generator of terms
%o A307878     blist, m = tuple(), 1
%o A307878     yield from blist
%o A307878     while True:
%o A307878         yield (blist := tuple(accumulate(reversed(blist),initial=m)))[-1]
%o A307878         m *= 3
%o A307878 A307878_list = list(islice(A307878_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A307878 Column k=3 of A292975.
%Y A307878 Cf. A000111, A000244, A000752, A307879.
%K A307878 nonn
%O A307878 0,2
%A A307878 _Ilya Gutkovskiy_, Jun 04 2019