cp's OEIS Frontend

A337446 E.g.f.: exp(2*x) * (BesselI(0,2*x) - BesselI(1,2*x)) / (sec(x) + tan(x)).

%I A337446 #8 Jun 11 2022 11:45:59
%S A337446 1,0,1,0,3,-9,5,-235,35,-5939,10773,-199746,961521,-10506833,82135911,
%T A337446 -836458064,8282576627,-90730736923,1034615625645,-12538466040640,
%U A337446 159529541334325,-2133316798885373,29875632576041747,-437461119834677379,6683837093985315589
%N A337446 E.g.f.: exp(2*x) * (BesselI(0,2*x) - BesselI(1,2*x)) / (sec(x) + tan(x)).
%C A337446 Inverse boustrophedon transform of Catalan numbers.
%H A337446 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A337446 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A000108(k) * A000111(n-k).
%t A337446 nmax = 24; CoefficientList[Series[Exp[2 x] (BesselI[0, 2 x] - BesselI[1, 2 x])/(Sec[x] + Tan[x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A337446 t[n_, 0] := CatalanNumber[n]; t[n_, k_] := t[n, k] = t[n, k - 1] - t[n - 1, n - k]; a[n_] := t[n, n]; Table[a[n], {n, 0, 24}]
%o A337446 (Python)
%o A337446 from itertools import islice, count, accumulate
%o A337446 from operator import sub
%o A337446 def A337446_gen(): # generator of terms
%o A337446     blist, c = tuple(), 1
%o A337446     for i in count(0):
%o A337446         yield (blist := tuple(accumulate(reversed(blist),func=sub,initial=c)))[-1]
%o A337446         c = c*(4*i+2)//(i+2)
%o A337446 A337446_list = list(islice(A337446_gen(),30)) # _Chai Wah Wu_, Jun 11 2022
%Y A337446 Cf. A000108, A000111, A000753.
%K A337446 sign
%O A337446 0,5
%A A337446 _Ilya Gutkovskiy_, Aug 27 2020