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A231200 Boustrophedon transform of even numbers.

%I A231200 #18 Jun 12 2022 10:19:53
%S A231200 0,2,8,24,72,240,924,4116,20944,119952,763540,5346748,40845816,
%T A231200 338041704,3012855356,28770647220,293055401888,3171602665696,
%U A231200 36343889387172,439607533130732,5597256953340360,74829813397495128,1048039052970587788,15345654816688856484
%N A231200 Boustrophedon transform of even numbers.
%H A231200 Reinhard Zumkeller, <a href="/A231200/b231200.txt">Table of n, a(n) for n = 0..400</a>
%H A231200 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>
%H A231200 J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A 44-54 1996 (<a href="http://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>).
%H A231200 Wikipedia, <a href="http://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon_transform</a>
%H A231200 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A231200 a(n) = Sum_{k=0..n} A109449(n,k)*k*2.
%F A231200 a(n) = 2*A231179(n).
%F A231200 E.g.f.: 2*x*exp(x)*(sec(x) + tan(x)). - _Ilya Gutkovskiy_, Sep 27 2017
%t A231200 T[n_, k_] := SeriesCoefficient[(1+Sin[x])/Cos[x], {x, 0, n-k}] n!/k!;
%t A231200 a[n_] := 2 Sum[k T[n, k], {k, 0, n}];
%t A231200 Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Jun 28 2019 *)
%o A231200 (Haskell)
%o A231200 a231200 n = sum $ zipWith (*) (a109449_row n) $ [0, 2 ..]
%o A231200 (Python)
%o A231200 from itertools import accumulate, count, islice
%o A231200 def A231200_gen(): # generator of terms
%o A231200     blist = tuple()
%o A231200     for i in count(0,2):
%o A231200         yield (blist := tuple(accumulate(reversed(blist),initial=i)))[-1]
%o A231200 A231200_list = list(islice(A231200_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A231200 Cf. A005843, A000754.
%K A231200 nonn
%O A231200 0,2
%A A231200 _Reinhard Zumkeller_, Nov 05 2013