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%I #29 Jun 11 2022 20:21:01
%S 0,1,4,12,36,120,462,2058,10472,59976,381770,2673374,20422908,
%T 169020852,1506427678,14385323610,146527700944,1585801332848,
%U 18171944693586,219803766565366,2798628476670180,37414906698747564,524019526485293894,7672827408344428242
%N Boustrophedon transform of nonnegative integers, cf. A001477.
%H Reinhard Zumkeller, <a href="/A231179/b231179.txt">Table of n, a(n) for n = 0..400</a>
%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>
%H 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 Wikipedia, <a href="http://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>
%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F a(n) = A231200(n)/2.
%F a(n) = Sum_{k=1..n} k * A109449(n,k).
%F E.g.f.: x*exp(x)*(sec(x)+tan(x)). (After Sergei N. Gladkovskii in A000660.) - _Peter Luschny_, Oct 28 2014
%F a(n) = A000660(n) - A000111(n). - _Sergei N. Gladkovskii_, Oct 28 2014
%F a(n) ~ n! * exp(Pi/2) * 2^(n+1) / Pi^n. - _Vaclav Kotesovec_, Jun 12 2015
%t a[n_] := n! SeriesCoefficient[x Exp[x] (1+Sin[x]) / Cos[x], {x, 0, n}];
%t Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Jul 30 2018, after _Peter Luschny_ *)
%o (Haskell)
%o a231179 n = sum $ zipWith (*) (a109449_row n) [0..]
%o (Python)
%o from itertools import count, islice, accumulate
%o def A231179_gen(): # generator of terms
%o blist = tuple()
%o for i in count(0):
%o yield (blist := tuple(accumulate(reversed(blist),initial=i)))[-1]
%o A231179_list = list(islice(A231179_gen(),30)) # _Chai Wah Wu_, Jun 11 2022
%Y Cf. A000111, A000737, A000660, A109449, A231200.
%K nonn
%O 0,3
%A _Reinhard Zumkeller_, Nov 05 2013
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