%I #40 Jun 12 2022 12:13:48
%S 1,5,18,57,180,617,2400,10717,54544,312353,1988104,13921501,106350816,
%T 880162337,7844596536,74910367309,763030711936,8257927397569,
%U 94628877364936,1144609672707741,14573622985067744,194834987492011649,2728787718495477144,39955604972310966797
%N Boustrophedon transform of squares.
%H Reinhard Zumkeller, <a href="/A000745/b000745.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 a(n) ~ n! * (6 + Pi + 4/Pi) * exp(Pi/2) * 2^n / Pi^n. - _Vaclav Kotesovec_, Jun 12 2015
%F E.g.f.: exp(x)*(x^2 + 3*x + 1)*(1+sin(x))/cos(x). - _Vaclav Kotesovec_, Jun 12 2015
%t CoefficientList[Series[E^(x)*(x^2+3*x+1)*(1+Sin[x])/Cos[x], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jun 12 2015 *)
%t t[n_, 0] := (n + 1)^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 (Haskell)
%o a000745 n = sum $ zipWith (*) (a109449_row n) $ tail a000290_list
%o -- _Reinhard Zumkeller_, Nov 03 2013
%o (Python)
%o from itertools import accumulate, count, islice
%o def A000745_gen(): # generator of terms
%o blist, c = tuple(), 1
%o for i in count(1):
%o yield (blist := tuple(accumulate(reversed(blist),initial=c)))[-1]
%o c += 2*i+1
%o A000745_list = list(islice(A000745_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y Cf. A000290, A000697.
%K nonn
%O 0,2
%A _N. J. A. Sloane_