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A306799 Expansion of e.g.f. (sec(x) + tan(x))*(BesselI(0,2*x) + BesselI(1,2*x)).

%I A306799 #25 Jun 11 2022 20:21:34
%S A306799 1,2,5,14,43,151,597,2701,13795,79129,503693,3527292,26945081,
%T A306799 222997659,1987492223,18979143358,193319844179,2092211006561,
%U A306799 23974970862885,289995870991594,3692342091149853,49362977658760079,691359846917532235,10123067013673200297,154669070822937580645
%N A306799 Expansion of e.g.f. (sec(x) + tan(x))*(BesselI(0,2*x) + BesselI(1,2*x)).
%C A306799 Boustrophedon transform of A001405.
%H A306799 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%t A306799 nmax = 24; CoefficientList[Series[(Sec[x] + Tan[x]) (BesselI[0, 2 x] + BesselI[1, 2 x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A306799 t[n_, 0] := Binomial[n, Floor[n/2]]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 25, 0]
%o A306799 (Python)
%o A306799 from itertools import accumulate, count, islice
%o A306799 def A306799_gen(): # generator of terms
%o A306799     blist, a  = tuple(), 1
%o A306799     for i in count(1):
%o A306799         yield (blist := tuple(accumulate(reversed(blist),initial=a)))[-1]
%o A306799         a = 2*a*i//(i+1) if i & 1 else 2*a
%o A306799 A306799_list = list(islice(A306799_gen(),30)) # _Chai Wah Wu_, Jun 11 2022
%Y A306799 Cf. A000111, A000753, A001405.
%K A306799 nonn
%O A306799 0,2
%A A306799 _Ilya Gutkovskiy_, Apr 16 2019