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A000674 Boustrophedon transform of 1, 2, 2, 2, 2, ...

%I A000674 #43 Jun 11 2022 15:55:55
%S A000674 1,3,7,16,43,138,527,2346,11943,68418,435547,3050026,23300443,
%T A000674 192835698,1718682167,16412205306,167173350543,1809239622978,
%U A000674 20732358910387,250773962554186,3192953259262243,42686640718266258,597853508941160207
%N A000674 Boustrophedon transform of 1, 2, 2, 2, 2, ...
%H A000674 Reinhard Zumkeller, <a href="/A000674/b000674.txt">Table of n, a(n) for n = 0..400</a>
%H A000674 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>.
%H A000674 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 A000674 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%H A000674 Wikipedia, <a href="https://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>.
%H A000674 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A000674 a(n) = Sum_{k=0..n} A109449(n,k)*A040000(k). - _Reinhard Zumkeller_, Nov 04 2013
%F A000674 E.g.f.: (sec(x) + tan(x))*(2*exp(x) - 1). - _Sergei N. Gladkovskii_, Oct 28 2014
%F A000674 Binomial convolution of A000111 and A040000. - _Michael Somos_, Oct 30 2014
%F A000674 a(n) ~ n! * (2*exp(Pi/2)-1) * 2^(n+2) / Pi^(n+1). - _Vaclav Kotesovec_, Jun 12 2015
%e A000674 G.f. = 1 + 3*x + 7*x^2 + 16*x^3 + 43*x^4 + 138*x^5 + 527*x^6 + 2346*x^7 + ...
%t A000674 With[{nn=30},CoefficientList[Series[(Sec[x]+Tan[x])(2Exp[x]-1),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 04 2015 *)
%o A000674 (Haskell)
%o A000674 a000674 n = sum $ zipWith (*) (a109449_row n) (1 : repeat 2)
%o A000674 -- _Reinhard Zumkeller_, Nov 04 2013
%o A000674 (Python)
%o A000674 from itertools import accumulate, islice
%o A000674 def A000674_gen(): # generator of terms
%o A000674     yield 1
%o A000674     blist = (1,)
%o A000674     while True:
%o A000674         yield (blist := tuple(accumulate(reversed(blist),initial=2)))[-1]
%o A000674 A000674_list = list(islice(A000674_gen(),30)) # _Chai Wah Wu_, Jun 11 2022
%Y A000674 Cf. A000111, A040000, A109449.
%K A000674 nonn
%O A000674 0,2
%A A000674 _N. J. A. Sloane_, _Simon Plouffe_
%E A000674 More terms from _Sean A. Irvine_, Feb 20 2011