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A000697 Boustrophedon transform of 1, 1, 4, 9, 16, ...

%I A000697 #51 Jun 12 2022 12:00:51
%S A000697 1,2,7,26,89,316,1243,5564,28321,162160,1032051,7226636,55206161,
%T A000697 456886912,4072080587,38885496092,396084390849,4286637591872,
%U A000697 49121248360291,594159600856332,7565074996215025,101137602761945440
%N A000697 Boustrophedon transform of 1, 1, 4, 9, 16, ...
%H A000697 Reinhard Zumkeller, <a href="/A000697/b000697.txt">Table of n, a(n) for n = 0..400</a>
%H A000697 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>.
%H A000697 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 A000697 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%H A000697 Wikipedia, <a href="https://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>.
%H A000697 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A000697 E.g.f.: (1 + exp(x)*x*(1 + x))*(sec(x) + tan(x)). - _Sergei N. Gladkovskii_, Oct 29 2014
%F A000697 a(n) ~ n! * (4 + exp(Pi/2)*Pi*(2 + Pi)) * 2^n / Pi^(n+1). - _Vaclav Kotesovec_, Jun 12 2015
%t A000697 t[n_, 0] := If[n==0, 1, n^2]; 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 A000697 (Haskell)
%o A000697 a000697 n = sum $ zipWith (*) (a109449_row n) (1 : tail a000290_list)
%o A000697 -- _Reinhard Zumkeller_, Nov 04 2013
%o A000697 (Python)
%o A000697 from itertools import accumulate, count, islice
%o A000697 def A000697_gen(): # generator of terms
%o A000697     yield 1
%o A000697     blist, m = (1,), 1
%o A000697     for i in count(1):
%o A000697         yield (blist := tuple(accumulate(reversed(blist),initial=m)))[-1]
%o A000697         m += 2*i+1
%o A000697 A000697_list = list(islice(A000697_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A000697 Cf. A000290, A000745, A109449.
%K A000697 nonn
%O A000697 0,2
%A A000697 _N. J. A. Sloane_, _Simon Plouffe_