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

%I

%S 1,2,7,26,89,316,1243,5564,28321,162160,1032051,7226636,55206161,

%T 456886912,4072080587,38885496092,396084390849,4286637591872,

%U 49121248360291,594159600856332,7565074996215025,101137602761945440

%N Boustrophedon transform of 1, 1, 4, 9, 16, ...

%H Reinhard Zumkeller, <a href="/A000697/b000697.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 on 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 N. J. A. Sloane, <a href="/transforms.txt">Transforms</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 E.g.f.: ( 1 + exp(x)*x*(1+x) )*(sec(x)+tan(x)). - _Sergei N. Gladkovskii_, Oct 29 2014

%F a(n) ~ n! * (4 + exp(Pi/2)*Pi*(2+Pi)) * 2^n / Pi^(n+1). - _Vaclav Kotesovec_, Jun 12 2015

%t 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-Fran├žois Alcover_, Feb 12 2016 *)

%o (Haskell)

%o a000697 n = sum $ zipWith (*) (a109449_row n) (1 : tail a000290_list)

%o -- _Reinhard Zumkeller_, Nov 04 2013

%Y Cf. A109449, A000290, A000745.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, _Simon Plouffe_

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Last modified February 21 14:36 EST 2018. Contains 299414 sequences. (Running on oeis4.)