%I #47 Jun 12 2022 12:01:03
%S 1,4,12,33,96,317,1218,5425,27608,158129,1006574,7048657,53847420,
%T 445643681,3971876930,37928628529,386337833232,4181155148673,
%U 47912508680086,579538956964241,7378919177090244,98648882783190305
%N Boustrophedon transform of odd numbers.
%H Reinhard Zumkeller, <a href="/A000754/b000754.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 (1996), 44-54 (<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 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%H Wikipedia, <a href="https://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 From _Reinhard Zumkeller_, Nov 02 2013: (Start)
%F a(n) = Sum_{k=0..n} A116666(n+1,k)*A000111(n-k).
%F a(n) = Sum_{k=0..n} A109449(n,k)*(2*k + 1). (End)
%F E.g.f.: (sec(x) + tan(x))*exp(x)*(2*x + 1). - _Sergei N. Gladkovskii_, Oct 30 2014
%F a(n) ~ n! * (Pi+1) * exp(Pi/2) * 2^(n+2) / Pi^(n+1). - _Vaclav Kotesovec_, Oct 30 2014
%t CoefficientList[Series[(Sec[x]+Tan[x])*E^x*(2*x+1), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Oct 30 2014 after _Sergei N. Gladkovskii_ *)
%t t[n_, 0] := 2n + 1; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 30, 0] (* _Jean-François Alcover_, Feb 12 2016 *)
%o (Haskell)
%o a000754 n = sum $ zipWith (*) (a109449_row n) [1, 3 ..]
%o -- _Reinhard Zumkeller_, Nov 02 2013
%o (Python)
%o from itertools import accumulate, count, islice
%o def A000754_gen(): # generator of terms
%o blist = tuple()
%o for i in count(1,2):
%o yield (blist := tuple(accumulate(reversed(blist),initial=i)))[-1]
%o A000754_list = list(islice(A000754_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y Cf. A005408.
%K nonn,nice,easy
%O 0,2
%A _N. J. A. Sloane_