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A307879 Expansion of e.g.f. exp(4*x)*(sec(x) + tan(x)).

%I A307879 #30 Jun 12 2022 09:39:39
%S A307879 1,5,25,126,645,3380,18285,103036,610345,3833540,25714345,185107596,
%T A307879 1433220045,11932724900,106613406405,1019012112556,10382757537745,
%U A307879 112378069315460,1287787864054465,15576862520435916,198330820236011445,2651486893149253220,37135749401704458525
%N A307879 Expansion of e.g.f. exp(4*x)*(sec(x) + tan(x)).
%C A307879 Boustrophedon transform of A000302 (powers of 4).
%H A307879 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%t A307879 nmax = 22; CoefficientList[Series[Exp[4 x] (Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A307879 t[n_, 0] := 4^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 A307879 (Python)
%o A307879 from itertools import accumulate, islice
%o A307879 def A307879_gen(): # generator of terms
%o A307879     blist, m = tuple(), 1
%o A307879     yield from blist
%o A307879     while True:
%o A307879         yield (blist := tuple(accumulate(reversed(blist),initial=m)))[-1]
%o A307879         m *= 4
%o A307879 A307879_list = list(islice(A307879_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A307879 Column k=4 of A292975.
%Y A307879 Cf. A000111, A000302, A000752, A307878.
%K A307879 nonn
%O A307879 0,2
%A A307879 _Ilya Gutkovskiy_, Jun 04 2019