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A306822 Expansion of e.g.f. (sec(x) + tan(x))*exp(2*x)*BesselI(0,2*x).

%I A306822 #22 May 04 2024 12:19:41
%S A306822 1,3,11,46,207,988,4989,26734,152827,937212,6192741,44191654,
%T A306822 340575513,2829201638,25252605283,241269232186,2457951274627,
%U A306822 26602476272908,304845053785469,3687342610303174,46948693772419597,627657623728640182,8790742273959180703,128716280124796774354
%N A306822 Expansion of e.g.f. (sec(x) + tan(x))*exp(2*x)*BesselI(0,2*x).
%C A306822 Boustrophedon transform of central binomial coefficients (A000984).
%H A306822 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A306822 a(n) ~ BesselI(0, Pi) * 2^(n + 5/2) * n^(n + 1/2) / (Pi^(n + 1/2) * exp(n - Pi)). - _Vaclav Kotesovec_, May 04 2024
%t A306822 nmax = 23; CoefficientList[Series[(Sec[x] + Tan[x]) Exp[2 x] BesselI[0, 2 x], {x, 0, nmax}], x] Range[0, nmax]!
%t A306822 t[n_, 0] := Binomial[2 n, n]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 24, 0]
%o A306822 (Python)
%o A306822 from itertools import count, islice, accumulate
%o A306822 def A306822_gen(): # generator of terms
%o A306822     blist, m = tuple(), 1
%o A306822     for i in count(1):
%o A306822         yield (blist := tuple(accumulate(reversed(blist),initial=m)))[-1]
%o A306822         m = m*(4*i-2)//i
%o A306822 A306822_list = list(islice(A306822_gen(),20)) # _Chai Wah Wu_, Jun 11 2022
%Y A306822 Cf. A000111, A000753, A000984.
%K A306822 nonn
%O A306822 0,2
%A A306822 _Ilya Gutkovskiy_, Apr 16 2019