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A306832 Expansion of e.g.f. (sec(x) + tan(x))*exp(x)*BesselI(0,2*x).

%I A306832 #26 Jun 12 2022 12:01:39
%S A306832 1,2,6,21,78,317,1394,6713,35518,207017,1326886,9314173,71206344,
%T A306832 589413593,5253411102,50166344891,510988365078,5530178925273,
%U A306832 63371129667726,766522745352829,9759669811328648,130477170753991277,1827415614960825342,26757484944450577839,408824255195817028276
%N A306832 Expansion of e.g.f. (sec(x) + tan(x))*exp(x)*BesselI(0,2*x).
%C A306832 Boustrophedon transform of central trinomial coefficients (A002426).
%H A306832 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%t A306832 nmax = 24; CoefficientList[Series[(Sec[x] + Tan[x]) Exp[x] BesselI[0, 2 x], {x, 0, nmax}], x] Range[0, nmax]!
%t A306832 t[n_, 0] := 3^n Hypergeometric2F1[ 1/2, -n, 1, 4/3]; 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 A306832 (Python)
%o A306832 from itertools import count, accumulate, islice
%o A306832 def A306832_gen(): # generator of terms
%o A306832     blist, a, b = (1,), 1, 1
%o A306832     yield from blist
%o A306832     for i in count(2):
%o A306832         yield (blist := tuple(accumulate(reversed(blist),initial=b)))[-1]
%o A306832         a, b = b, (b*(2*i-1)+(3*i-3)*a)//i
%o A306832 A306832_list = list(islice(A306832_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A306832 Cf. A000111, A002426, A306822.
%K A306832 nonn
%O A306832 0,2
%A A306832 _Ilya Gutkovskiy_, Apr 16 2019